Application of Singular Spectrum-based Change-point
Analysis to EMG Event Detection
By
Lev Vaisman
A thesis submitted in conformity with the requirements for the degree of Master of Applied Science in
Biomedical Engineering, Graduate Department of Institute of Biomaterials and Biomedical Engineering,
University of Toronto
Copyright © Lev Vaisman 2008
ii
Abstract
Name: Lev Vaisman,
MASc Thesis Title: Application of Singular Spectrum-based Change-point Analysis to EMG
Event Detection
Year of Convocation: 2008
Department: Institute of Biomaterials and Biomedical Engineering
University: University of Toronto
Electromyogram (EMG) is an established tool to study operation of neuromuscular systems. In
analysing EMG signals, accurate detection of the movement-related events in the signal is
frequently necessary. I explored the application of change-point detection algorithm proposed by
Moskvina et. al., 2003 to EMG event detection, and evaluated the technique’s performance
comparing it to two common threshold-based event detection methods and to the visual estimates
of the EMG events performed by trained practitioners in the field. The algorithm was
implemented in MATLAB and applied to EMG segments recorded from wrist and trunk
muscles. The quality and frequency of successful detection were assessed for all methods, using
the average visual estimate as the baseline, against which techniques were evaluated. The
application showed that the change-point detection can successfully locate multiple changes in
the EMG signal, but the maximum value of the detection statistic did not always identify the
muscle activation onset.
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Acknowledgements
First of all, I would like to thank my supervisor Professor Milos Popovic for his assistance,
support and advice throughout the entire time that I worked on this project. His
recommendations have guided my investigations while his explanations greatly improved my
understanding. I would also like to thank my regular committee members Professor Tom Chau
and Professor Berj Bardakjian for their valuable suggestions during the committee meetings.
Secondly, I would like to acknowledge the graduate students and postdoctoral fellows in the
Rehabilitation Engineering Laboratory at Lyndhurst Rehabilitation Center who helped me
throughout the project. Cesar Marquez-Chin introduced me to the EEG and EMG signal
processing techniques. Dr. Kei Masani and Vivian Sin provided me with the recordings from
trunk muscles, as well as with the diagrams describing the experiment, in which this data was
acquired. Also Dr. Masani as well as Dr. Noritaka Kawashima and Dr. Dmitry Sayenko assisted
me by providing the visual EMG onset estimates. Dr. Sayenko also provided the 3D diagram for
the electrodes placement for the wrist EMG data recordings. I am also very grateful to other
members of the lab, not listed here, for creating a very interesting and friendly environment to
work in, and their moral support throughout my project.
I would also like to thank Dr. Robert Chen and Eric Tsang from Toronto Western Hospital who
provided me with the wrist EMG recordings.
Finally, I would like to thank the IBBME and NSERC for providing me with the opportunity to
work on this project.
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Table of Contents
ABSTRACT.................................................................................................................................. II
ACKNOWLEDGEMENTS .......................................................................................................III
TABLE OF CONTENTS ........................................................................................................... IV
LIST OF ABBREVIATIONS ....................................................................................................VI
LIST OF EQUATIONS............................................................................................................ VII
LIST OF FIGURES .................................................................................................................VIII
LIST OF TABLES ....................................................................................................................... X
CHAPTER 1: INTRODUCTION................................................................................................ 1
1.1. MUSCLES TYPES AND PHYSIOLOGY ................................................................................. 1
1.2. ELECTROMYOGRAPHY ..................................................................................................... 2
1.2.1. Definition .................................................................................................................... 2
1.2.2. Recording.................................................................................................................... 2
1.2.3. Applications ................................................................................................................ 3
1.3. EMG PROCESSING AND PROBLEM OF MUSCLE CONTRACTION EVENTS DETECTION ....... 4
1.4. MOTIVATION FOR THE PROJECT PRESENTED IN THIS DOCUMENT..................................... 5
1.5. THESIS OUTLINE .............................................................................................................. 6
CHAPTER 2: LITERATURE REVIEW ................................................................................... 7
2.1. OVERVIEW OF ONSET OF EMG MOVEMENT-RELATED EVENTS DETECTION METHODS ... 7
2.1.1. Threshold-based Methods........................................................................................... 7
2.1.2. Denoising .................................................................................................................... 8
2.1.3. Model-based Methods................................................................................................. 9
2.2. OVERVIEW OF CHANGE-POINT ANALYSIS METHODS ..................................................... 10
2.2.1. Concepts, Definitions, Applications.......................................................................... 10
2.2.2. Methods of Change-point Analysis ........................................................................... 11
2.2.3. Review of Change-point Analysis Applications to Biological Signals...................... 13
2.3. SINGULAR SPECTRUM ANALYSIS (SSA) AND CHANGE-POINT DETECTION .................... 15
2.3.1. SSA Theory and Applications.................................................................................... 15
2.3.2. Change-point Detection Algorithm Based on SSA.................................................... 17
2.3.3. Why Choose the SSA-based Algorithm for this Study?............................................. 19
2.4. SUMMARY OF THE CHAPTER .......................................................................................... 20
CHAPTER 3: OBJECTIVES AND HYPOTHESIS................................................................ 21
3.1. OBJECTIVES ................................................................................................................... 21
3.2. HYPOTHESIS................................................................................................................... 21
CHAPTER 4: METHODS ......................................................................................................... 22
4.1. DATA ACQUISITION ....................................................................................................... 22
4.1.1. Wrist Extension Experiments .................................................................................... 22
4.1.2. Trunk Muscles Involved in Sitting............................................................................. 24
v
4.2. SSA-BASED CHANGE-POINT DETECTION ALGORITHM PARAMETERS SELECTION AND
IMPLEMENTATION ...................................................................................................................... 25
4.2.1. Parameter Selection.................................................................................................. 25
a) Selecting lag M and window size m: Tests with Gaussian noise.................................. 26
b) Selection of the number of components L ..................................................................... 28
c) Selection of test interval parameters p and q ............................................................... 28
4.2.2. MATLAB Implementation ......................................................................................... 29
4.3. PROCESSING SET-UP ...................................................................................................... 30
4.3.1. Methods of EMG Movement-related Events Detection and Signal Pre-processing. 31
4.3.2. Application of Hodges&Bui Method......................................................................... 32
4.3.3. Application of Donoho’s Wavelet-based Denoising Method.................................... 33
4.3.4. Comparison of Onset Detection Methods. ................................................................ 34
4.4. SUMMARY OF THE CHAPTER .......................................................................................... 34
CHAPTER 5: RESULTS ........................................................................................................... 36
5.1. SAMPLE EVENT DETECTION IN WRIST AND TRUNK MUSCLE EMG ............................... 36
5.2. FREQUENCY OF SUCCESSFUL EMG MOVEMENT-RELATED EVENTS DETECTION BY
DIFFERENT METHODS IN WRIST MUSCLES ................................................................................ 38
5.3. FREQUENCY OF SUCCESSFUL EMG MOVEMENT-RELATED EVENTS DETECTION BY
DIFFERENT METHODS IN TRUNK MUSCLES................................................................................ 41
5.4. QUALITY OF MOVEMENT-RELATED EVENTS DETECTION BY DIFFERENT METHODS IN
WRIST MUSCLES........................................................................................................................ 43
5.5. QUALITY OF MOVEMENT-RELATED EVENTS ONSET DETECTION BY DIFFERENT METHODS
IN TRUNK MUSCLES ................................................................................................................... 45
5.6. SUMMARY OF THE CHAPTER .......................................................................................... 46
CHAPTER 6: DISCUSSION ..................................................................................................... 48
6.1. BENEFITS OF CHANGE-POINT DETECTION IN THE EMG PROCESSING APPLICATION ...... 48
6.2. LIMITATIONS OF THE CHANGE-POINT DETECTION IN THE EMG PROCESSING
APPLICATION ............................................................................................................................. 49
6.3. ISSUES WORTHY OF FURTHER INVESTIGATION .............................................................. 51
6.4. SUMMARY OF THE CHAPTER .......................................................................................... 52
CHAPTER 7: CONCLUSION AND FUTURE WORK ......................................................... 53
APPENDICES............................................................................................................................. 61
APPENDIX A: CHANGE-POINT DETECTION ALGORITHM MATLAB IMPLEMENTATION.............. 61
APPENDIX B: SCRIPT TO INPUT THE VISUAL ESTIMATES OF THE EMG ONSETS WITH A MOUSE IN
MATLAB.................................................................................................................................. 64
APPENDIX C: HODGES&BUI ALGORITHM IMPLEMENTATION IN MATLAB ............................... 65
APPENDIX D: WAVELET-BASED DENOISING IMPLEMENTATION IN MATLAB........................... 66
APPENDIX E: AVERAGE ABSOLUTE DIFFERENCES PLOTS, KRUSKAL-WALLIS / ANOVA TABLES
AND MULTIPLE COMPARISONS PLOTS FOR WRIST MUSCLE EMG ............................................. 68
APPENDIX F: AVERAGE ABSOLUTE DIFFERENCES PLOTS, KRUSKAL-WALLIS / ANOVA TABLES
AND MULTIPLE COMPARISONS PLOTS FOR TRUNK MUSCLE EMG ............................................ 77
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List of Abbreviations
AGLR – approximated generalized likelihood ratio
AR – autoregressive model (also known as all-pole model)
ATP – adenosine triphosphate
CUSUM – cumulative sum
DGM – data generation mechanism
DGP – data generation process
EEG – electroencephalography, electroencephalogram
EKG – electrocardiogram
EMG – electromyography, electromyogram, electromyographic
LRF – linear recurrence formula
ME – myoelectric
MUAP – motor unit action potential
SNR – signal-to-noise ratio
SSA – singular spectrum analysis
SSM – state-space model
STN – subthalamic nucleus / nuclei
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List of Equations
EQUATION 1: KOLMOGOROV-SMIRNOV DETECTION STATISTIC ...................................................... 12
EQUATION 2: TRAJECTORY MATRIX FOR SINGULAR SPECTRUM ANALYSIS.................................... 16
EQUATION 3: RECONSTRUCTION OF SIGNAL AFTER SSA-DECOMPOSITION INTO COMPONENTS. .... 16
EQUATION 4: FORM OF THE PROCESS, WHICH CAN BE WELL REPRESENTED BY LINEAR RECURRENT
FORMULA ............................................................................................................................... 17
EQUATION 5: EQUATION OF THE TRAJECTORY MATRIX FOR SSA-BASED CHANGE-POINT DETECTION.
............................................................................................................................................... 18
EQUATION 6: EQUATION OF THE LAG-COVARIANCE MATRIX FOR SSA-BASED CHANGE-POINT
DETECTION............................................................................................................................. 18
EQUATION 7: EQUATION OF THE TEST MATRIX FOR SSA-BASED CHANGE-POINT DETECTION......... 18
EQUATION 8: EQUATION FOR DN STATISTIC ................................................................................... 19
EQUATION 9: EQUATION FOR CUSUM STATISTIC. ........................................................................ 19
EQUATION 10: EQUATION OF THE THRESHOLD FOR CHANGES IN SSA-BASED CHANGE-POINT
DETECTION............................................................................................................................. 19
EQUATION 11: EQUATION FOR VN USED IN MATLAB IMPLEMENTATION OF THE CHANGE-POINT
DETECTION ALGORITHM. ........................................................................................................ 30
EQUATION 12: ALTERNATIVE FORMULA FOR VN CALCULATION ..................................................... 30
EQUATION 13: ALTERNATIVE FORMULA FOR VN CALCULATION ..................................................... 30
EQUATION 14: ALTERNATIVE EQUATION OF THRESHOLD FOR CHANGES IN SSA-BASED CHANGE-
POINT DETECTION................................................................................................................... 30
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List of Figures FIGURE 1: DIAGRAM SHOWING ELECTRODES LOCATIONS FOR RECORDING OF EMG FROM EXTENSOR
CARPI RADIALIS MUSCLES. RECTANGLE IS THE LOCATION FOR RECORDING ELECTRODES AND
CIRCLE IS A PLACE OF REFERENCE ELECTRODE. PROVIDED BY DR. D. SAYENKO, 2008.......... 23
FIGURE 2: DIRECTIONS OF PERTURBATION (SIN, 2007) .................................................................. 24
FIGURE 3: FRONT VIEW (LEFT) AND BACK VIEW (RIGHT) OF THE LOCATIONS OF EMG ELECTRODES
FOR TRUNK MUSCLES EMG RECORDINGS (SIN, 2007)............................................................ 25
FIGURE 4: TEST OF EFFECT OF LAG PARAMETER ON CHANGE-POINT DETECTION IN GAUSSIAN NOISE
(A) GAUSSIAN NOISE, 10,000 POINTS, MEAN 0, VAR 1, (B-D) RESULTS OF CHANGE-POINT
DETECTION WITH (B) LAG M=100, M=200, (C) M=50, M=100, (D) M=25, M=50. BLUE LINE IS
DETECTION STATISTIC, PINK LINE SHOWS THE THRESHOLD. NOTABLY, PLOT (B) SHOWS LESS
FALSE CHANGES DETECTED THAN PLOTS (C) AND (D), THUS SHOWING INCREASE OF ACCURACY
WITH LAG PARAMETER. .......................................................................................................... 27
FIGURE 5: SAMPLE DETECTION RESULTS FOR WRIST MUSCLE EMG (A) ORIGINAL EMG SIGNAL, (B)
DN DETECTION STATISTIC, (C) CUSUM DETECTION STATISTIC. RED CIRCLE MARKS THE
COMPUTED EMG MOVEMENT-RELATED EVENT ONSET. ......................................................... 36
FIGURE 6: SAMPLE DETECTION RESULTS FOR TRUNK MUSCLES EMG (A) ORIGINAL EMG SIGNAL,
(B) DN DETECTION STATISTIC, (C) CUSUM DETECTION STATISTIC. RED CIRCLE MARKS THE
COMPUTED EMG ONSET. ....................................................................................................... 37
FIGURE 7: DETECTION OF MOVEMENT-RELATED EVENT IN EMG SIGNAL CONTAMINATED BY
TREMOR. TOP PLOT SHOWS THE ORIGINAL RAW SIGNAL WITH TREMOR SPIKES TO WHICH
CHANGE-POINT ANALYSIS IS APPLIED. SECOND PLOT SHOWS THE FILTERED AND RECTIFIED
SIGNAL FROM WHICH THE HODGES-BUI ESTIMATE IS COMPUTED, AND WHICH DOES NOT HAVE
TREMOR SPIKES WHICH WERE REMOVED BY FILTERING, THUS PROVIDING THE BEST ESTIMATE.
THIRD PLOT SHOWS THE WAVELET-DENOISED SIGNAL FROM WHICH WAVELET-BASED
ESTIMATE WAS OBTAINED. LOWEST PLOT SHOWS THE CUSUM STATISTIC WITH THE CHANGES
DETECTED BOTH DUE TO TREMOR SPIKES AND DUE TO MOVEMENT-RELATED MUSCLE
ACTIVATION, WITH THE CHANGES DUE TO TREMOR INFLUENCING THE CHANGE-POINT
STATISTIC STRONGER. ............................................................................................................ 40
FIGURE 8: AN EXAMPLE OF EMG EVENT MISDETECTION BY THE CHANGE-POINT ANALYSIS
ALGORITHM IN TRUNK EMG. TOP PLOT SHOWS THE ORIGINAL SIGNAL FROM ONE OF THE
TRUNK MUSCLES. SECOND PLOT SHOWS THE FILTERED AND RECTIFIED SIGNAL FROM WHICH
THE HODGES-BUI ESTIMATE IS COMPUTED. THIRD PLOT SHOWS THE WAVELET-DENOISED
SIGNAL FROM WHICH WAVELET-BASED ESTIMATE WAS OBTAINED. LOWEST PLOT SHOWS THE
CUSUM STATISTIC WITH MULTIPLE CHANGES DETECTED IN SEQUENCE WITH SOME OF THE
LATER CHANGES HAVING BIGGER INFLUENCE ON THE DETECTION STATISTIC THAN THE
EARLIER ONES, ALTHOUGH EARLIER SMALLER CHANGES ARE UNANIMOUSLY IDENTIFIED BY
VISUAL ESTIMATORS AS THE ONSET OF MOVEMENT-RELATED EVENT..................................... 42
FIGURE 9: AAA1 AVERAGE ABSOLUTE DIFFERENCES .................................................................. 68
FIGURE 10: AAA1 MULTIPLE COMPARISONS TEST ....................................................................... 68
FIGURE 11: AAA2 AVERAGE ABSOLUTE DIFFERENCES ................................................................ 69
FIGURE 12: AAA2 MULTIPLE COMPARISONS TEST ....................................................................... 69
FIGURE 13: AAA3 AVERAGE ABSOLUTE DIFFERENCES ................................................................ 70
FIGURE 14: AAA3 MULTIPLE COMPARISONS TEST ....................................................................... 70
FIGURE 15: AAA4 AVERAGE ABSOLUTE DIFFERENCES ................................................................ 71
FIGURE 16: AAA4 MULTIPLE COMPARISONS TEST ....................................................................... 71
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FIGURE 17: AAA5 AVERAGE ABSOLUTE DIFFERENCES ................................................................ 72
FIGURE 18: AAA5 MULTIPLE COMPARISONS TEST ....................................................................... 72
FIGURE 19: AAA6 AVERAGE ABSOLUTE DIFFERENCES ................................................................ 73
FIGURE 20: AAA6 MULTIPLE COMPARISONS TEST ....................................................................... 73
FIGURE 21: AAA7 AVERAGE ABSOLUTE DIFFERENCES ................................................................ 74
FIGURE 22: AAA7 MULTIPLE COMPARISONS TEST ....................................................................... 74
FIGURE 23: AAA8 AVERAGE ABSOLUTE DIFFERENCES ................................................................ 75
FIGURE 24: AAA8 MULTIPLE COMPARISONS TEST ....................................................................... 75
FIGURE 25: AAA9 AVERAGE ABSOLUTE DIFFERENCES ................................................................ 76
FIGURE 26: AAA9 MULTIPLE COMPARISONS TEST ....................................................................... 76
FIGURE 27: SUBJECT 1 AVERAGE ABSOLUTE DIFFERENCES .......................................................... 77
FIGURE 28: SUBJECT 1 MULTIPLE COMPARISONS TEST ................................................................. 77
FIGURE 29: SUBJECT 2 AVERAGE ABSOLUTE DIFFERENCES .......................................................... 78
FIGURE 30: SUBJECT 2 MULTIPLE COMPARISONS TEST................................................................. 78
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List of Tables TABLE 1: FREQUENCY OF SUCCESSFUL MOVEMENT-RELATED EVENT DETECTION IN WRIST EMG
FOR DIFFERENT COMPUTER METHODS. FILENAMES SHOW THE CODED PARTICIPANT ID (I.E.
AAA1) WHETHER RECORDING WAS OFF MEDICATION (OFFMED) OR ON MEDICATION
(ONMED), AND WHETHER THE RECORDED TASK WAS INTERNALLY (INT) OR EXTERNALLY
(EXT) TRIGGERED. ................................................................................................................ 38
TABLE 2: FREQUENCY OF SUCCESSFUL MOVEMENT-RELATED EVENT DETECTION IN TRUNK EMG
FOR DIFFERENT COMPUTER METHODS. FILENAMES SHOW THE PARTICIPANT ID AND
DIRECTIONS OF PERTURBATION (MIDDLE DIGIT OF THE NUMERICAL CODE) ACCORDING TO
FIGURE 2 FROM THE SUBSECTION 4.1.2.................................................................................. 41
TABLE 3: QUALITY OF MOVEMENT-RELATED EVENTS ONSET DETECTION ASSESSED BY MEAN
RANKS OF AVERAGE ABSOLUTE DIFFERENCES BETWEEN VISUAL ESTIMATES AND COMPUTER
METHODS IN WRIST EMG SIGNALS (MEAN RANK ± STANDARD ERROR). FILENAMES SHOW THE
CODED PARTICIPANT ID (I.E. AAA1). ALL THE RECORDINGS WHOSE RESULTS ARE PRESENTED
IN THIS TABLE WERE EXTERNALLY TRIGGERED (EXT) AND WERE RECORDED OFF MEDICATION
(OFFMED) OR ON MEDICATION (ON) ................................................................................... 44
TABLE 4: QUALITY OF MOVEMENT-RELATED EVENTS ONSET DETECTION ASSESSED BY SPEARMAN
RANK COEFFICIENTS BETWEEN VISUAL ESTIMATES AND COMPUTER METHODS IN WRIST
EMG SIGNALS. FILENAMES SHOW THE CODED PARTICIPANT ID (I.E. AAA1). ALL THE
RECORDINGS WHOSE RESULTS ARE PRESENTED IN THIS TABLE WERE EXTERNALLY TRIGGERED
(EXT) AND WERE RECORDED OFF MEDICATION (OFFMED) OR ON MEDICATION (ON) ......... 45
TABLE 5: QUALITY OF MOVEMENT-RELATED EVENT ONSET DETECTION ASSESSED BY MEAN
RANKS OF AVERAGE ABSOLUTE DIFFERENCES BETWEEN VISUAL ESTIMATES AND COMPUTER
METHODS IN TRUNK EMG SIGNALS (MEAN RANK ± STANDARD ERROR) ............................... 46
TABLE 6: QUALITY OF MOVEMENT-RELATED EVENT ONSET DETECTION ASSESSED BY SPEARMAN
RANK COEFFICIENTS BETWEEN VISUAL ESTIMATES AND COMPUTER METHODS IN TRUNK
EMG SIGNALS ....................................................................................................................... 46
TABLE 7: AAA1 KRUSKAL-WALLIS ANOVA............................................................................... 68
TABLE 8: AAA2 KRUSKAL-WALLIS ANOVA............................................................................... 69
TABLE 9: AAA3 KRUSKAL-WALLIS ANOVA............................................................................... 70
TABLE 10: AAA4 KRUSKAL-WALLIS ANOVA............................................................................. 71
TABLE 11: AAA5 KRUSKAL-WALLIS ANOVA............................................................................. 72
TABLE 12: AAA6 KRUSKAL-WALLIS ANOVA............................................................................. 73
TABLE 13: AAA7 KRUSKAL-WALLIS ANOVA............................................................................. 74
TABLE 14: AAA8 KRUSKAL-WALLIS ANOVA............................................................................. 75
TABLE 15: AAA9 KRUSKAL-WALLIS ANOVA............................................................................. 76
TABLE 16: SUBJECT 1 KRUSKAL-WALLIS ANOVA ...................................................................... 77
TABLE 17: SUBJECT 2 KRUSKAL-WALLIS ANOVA....................................................................... 78
1
Chapter 1: Introduction
1.1. Muscles Types and Physiology
There are three types of muscles in the human body: skeletal, smooth and cardiac muscles.
Skeletal muscles represent about 40% of the body, while the other types represent about 10%.
Skeletal muscles are involved in locomotion, are attached to bones by tendons, and are typically
under voluntary control. Smooth muscles form a lining of gastro-intestinal tract, urinary tract and
blood vessels. Cardiac muscle forms the bulk of the heart. Smooth and cardiac muscle are under
involuntary control (Ethier et. al., 2007, Guiton et. al., 2000).
Skeletal muscles are composed of many muscle fibers, which are innervated by the nerves
originating from the motoneurons of the spinal cord and brain stem. Each motoneuron innervates
multiple muscle fibers. All muscle fibers innervated by the same motoneuron are called a motor
unit. Muscle fibers have a cell membrane called sarcolemma, which contains numerous
acetylcholine-gated channels. The area where a nerve comes into contact with the muscle fiber is
called a neuromuscular junction (Guiton et. al., 2000).
Muscle fibers consist of hundreds to thousands of myofibrils. Myofibrils contain multiple
actin and myosin filaments which are the proteins carrying out the muscle contraction.
Myofibrils inside the muscle fibers are in an intracellular matrix called sarcoplasm, which
contains large quantities of ions, sarcoplasmic reticulum, storing calcium, and mitochondria,
which generate energy in form of adenosine triphosphate (ATP), which is needed in large
quantities for muscle operation (Guiton et. al., 2000).
When a signal in form of an action potential from the nerve reaches the muscle, a small
amount of neurotransmitter substance acetylcholine is released at the neuromuscular junction.
Acetylcholine makes acetylcholine-gated channels in the sarcolemma to open, which allows the
influx of sodium ions into the muscle fiber, thus initiating an action potential. The action
potential propagates along the muscle and penetrates deep into the muscle where it causes the
release of calcium from sarcoplasmic reticulum. Calcium ions enable the interaction between
actin and myosin filaments of myofibrils, allowing them to slide one along other, thus enabling
the actual muscle contraction. Shortly after that, calcium ions are forced back into sarcoplasmic
2
reticulum by the calcium pump, where they remain until a new action potential arrives at the
muscle. This removal of calcium ions stops muscle contraction (Guiton et. al., 2000).
1.2. Electromyography
1.2.1. Definition
Electromyography (EMG) is a technique used for recording of action potentials generated by
the muscles (Cooper et. al., 2005). The action potentials of all muscle fibers that belong to a
motor unit summate spatially and temporally to create a so-called motor unit action potential
(MUAP). The algebraic summation of all the MUAPs active at a certain moment in time in the
vicinity of the recording site yields an EMG or sometimes also called a myoelectric signal (ME)
(de Luca, 1979).
1.2.2. Recording
Very first investigations of electrical activity in the muscles were performed by Luigi
Galvani and Alessandro Volta in the second half of 18th
century. In 1929 Adrian and Bronk
introduced a concentric needle electrode allowing recording of EMG from individual motor
units. Before the 1940s EMG recordings remained very expensive because all researchers used
custom-made equipment, but after the introduction of monopolar electrodes in 1944 by Jasper
and Notman, and nerve conduction studies by Dawson and Scott in 1949, EMG became feasible
to use as a clinical tool (Cooper et. al., 2005).
EMG can be recorded with both deep needle electrodes and surface electrodes. Needle
electrodes allow deriving individual MUAPs from recordings of a small amount of fibers. By
means of such electrodes one can investigate loss of nerve supply to the muscles, diseases
affecting muscle fibers and neuromuscular junctions. One can also study motor unit recruitment
and firing patterns. However, this recording approach is invasive, for it requires the insertion of
the needle into the muscle. On the other hand, surface EMG is non-invasive. Although one
cannot record single muscle fiber activity using surface EMG electrodes, one can obtain
information on temporal patterns of muscle activity, fatigue and other aspects of muscle
3
behaviour. For example, surface EMG is useful for estimation of muscle-fiber conduction
velocity, length and orientation of the fibers, and MUAP propagation (Trontelj et. al., 2004).
There are many factors that influence EMG signal recording. There are anatomical and
physiological factors. Anatomical factors include thickness of skin and subcutaneous tissue
layers, size and distribution of motor units, number and length of muscle fibers in motor units.
The placement, size and shape of electrodes, as well as their orientation with respect to the
muscle fiber alignment could also be important. Physiological factors including muscle fibers’
and motor units’ conduction velocities, type of contraction, motor unit synchronization, as well
as blood flow, temperature and intramuscular pH could also affect the EMG. Besides that,
crosstalk between muscles is also important. Crosstalk refers to situations when the signal
recorded over one muscle is actually generated by another muscle. For example, when recording
EMG from the trunk muscles, EKG signal may interfere with the recorded muscle EMG. Also,
the noise from the EMG recording system can affect the results (Farina et. al., 2004, Merletti et.
al., 2001).
1.2.3. Applications
EMG has become a valuable tool in many applications, for example, in neurology,
ergonomics, rehabilitation medicine, and prostheses control.
Needle-electrode EMG can help diagnosing neurogenic and myopathic diseases by
measuring muscle activity at rest, number of motor units under voluntary control, and the
duration and amplitude of MUAPs (Rowland, 2000). Surface EMG is also useful in evaluating
patients with abnormal involuntary muscle activation, such as those in tremor or dystonia, and
patients with a weakness or paralysis (Zwarts et. al., 2004).
EMG was also used to investigate muscle fatigue in ergonomics related research studies, for
instance, during the use of hand tools, work at the assembly line and driving (Hagg et. al., 2004).
Furthermore, EMG was used to study muscle activation patterns during walking, running,
standing, sitting, etc. For example, studies of synergistic action of different muscles were
conducted during shoulder movements (Park et. al., 2008) and quiet standing posture control
(Krishnamoorthy et. al., 2003). EMG was also used to study various exercises such as, for
instance, weightlifting and skiing (Pearson et. al., 2002, Koyanagi et. al., 2006). In addition,
4
EMG was used to better understand the muscle fiber damage due to overuse and how muscle
recovers over time after overuse (Felici, 2004).
EMG signals are also being used to control powered prosthesis, i.e., myoelectric control of
upper or lower limb prostheses. The source of the input signal is a residual muscle remaining
after amputation. Contraction of one or more residual muscles using surface EMG electrodes can
be used to generate control signals for the prosthesis. In particular, the control signal is derived
from the myoelectric signal’s variance or signal pattern corresponding to a particular task or
function (Parker et. al., 2004).
1.3. EMG Processing and Problem of Muscle Contraction Events Detection
The recorded EMG signal is usually called raw EMG signal. Depending on the desired type
of analysis it is necessary to perform certain manipulations on the raw signal. For example,
common signal processing steps are removal of non-zero bias due to equipment noise, and
artefacts due to electrocardiogram (EKG) or heartbeat by filtering with highpass (McMulkin et.
al., 1998) or bandpass filters (Potvin et. al., 2004). To quantify the amount of muscle activity,
smoothing procedures are applied on rectified EMG signals, such as mean-absolute value
processing, root-mean-square processing or lowpass filtering (Clancy et. al., 2002; Kamen,
1996). Another technique commonly applied is normalization of EMG signals. This technique
basically expresses the level of muscle activity as a percentage of a reference EMG signal that is
obtained when a specific movement is performed (Mirka, 1991).
Detecting the onset of EMG movement-related event such as muscle contraction is another
frequently performed EMG processing task. It is important for several applications. Firstly, it is a
marker for the start of active control of the muscle (Stylianou, 2003, Staude et. al., 2001).
Secondly, it is important for the measurement of performance in so-called reaction time
experiments (Staude et. al., 2001, van Boxtel et. al., 1993) with external stimulus, i.e. when
subjects have to perform an action as soon as possible after they receive a corresponding
command. EMG onset is also commonly used for alignment of movement-related potentials in
electroencephalogram (EEG) and to divide the reaction time interval into motor and premotor
reaction time, which is important in neurology and psychophysiological applications (van Boxtel
et. al., 1993).
5
There are two main approaches for the detection of EMG events: visual (Hodges et. al., 2001,
Urquhart et. al., 2005) and algorithm-based (Staude et. al., 2001; Morey-Klapsing et. al., 2004).
A common criticism for the visual method is its subjectivity, and that the accuracy of the results
depend considerably on the experience of the person performing the EMG onset detection
(Micera et. al., 2001). For algorithm-based detection numerous algorithms have been proposed,
but there is no standardized method that is used to perform EMG onset detection (Hodges et. al.,
1996).
1.4. Motivation for the Project Presented in this Document
Originally the intent of my master’s degree project was to investigate ways of determining
the onset of movement in the recordings obtained from the basal ganglia. Namely, the objective
was to investigate if one can extract the onset of a movement using recordings obtained from the
deep brain stimulation electrodes that were implanted in the subthalamic nucleus of Parkinson’s
disease patients. If successful, this project would represent a first step towards developing a
brain-machine interface that will use deep brain recordings. Such a device would be useful, for
example, to control a neuroprosthesis device for restoration of movement in paralyzed patients.
One of the pre-processing steps for the brain signals analysis required computing the onsets
of movement based on the EMG signals that were recorded simultaneously with the deep brain
signals. The deep brain recordings were recorded while the patient was performing wrist
extensions followed by passive flexions. The segments of the brain signals were then extracted
using the onset of the wrist extensor muscle contraction. During the study the techniques of
change-point analysis, i.e., detection of changes in the signal, came to my attention. Change-
point detection is commonly used for time series analysis in various fields, and its applications
will be reviewed in subsequent sections. This approach seemed to show promise in the analysis
of movement-related changes in the brain signals. At the same time, it was observed that the
employed change-point detection procedure allowed a rather clean detection of changes in the
EMG signal and as a result the project goals changed from deep brain recordings analysis
towards exploring use of change-point detection technique for identification of EMG muscle
activation events onset and EMG signal processing.
Although various methods for detection of the onset of muscle contraction from the EMG
recording already exist, a method that is widely accepted yet needs to be developed. Therefore, I
6
have decided to explore use of the change-point detection analysis, which is rarely used in
biomedical engineering, as a method that could potentially be useful to identify onset of muscle
contraction from the EMG signals. The other purpose of this thesis was to test the usability of the
change-point detection analysis for processing biological signals.
1.5. Thesis Outline
Chapter 2 reviews the currently used detection algorithms for EMG movement-related
events, and change-point detection techniques and their applications to biological signals.
Chapter 3 states the objectives and hypotheses of this study. Chapter 4 describes the data
acquisition for wrist extension and perturbed sitting datasets used for the comparison of EMG
onset detection techniques. It also describes the singular spectrum analysis (SSA) signal
processing technique and its application for change-point detection algorithm. Approaches for
the parameters selection for the algorithm’s application to EMG signals are discussed too.
Chapter 5 presents the results of application of change-point detection method to the EMG
signals, and the comparison of computed EMG event onsets to those determined by other
detection methods, including basic thresholding algorithm, thresholding with wavelet-based
denoising, and visual detection. Chapter 6 discusses the results and the limitations of the change-
point detection approach. Chapter 7 summarizes the findings and provides concluding remarks
and recommendations for future work.
7
Chapter 2: Literature Review
In this chapter, the methods commonly used for EMG muscle activation events detection
will be presented. Also the main concepts related to the change-point detection problem will be
introduced, and the developed techniques in this field will be described. Also the theory for the
singular spectrum analysis based change-point detection algorithm will be presented in this
section in detail. The studies in which change-point detection was applied to the biological signal
processing will be discussed as well.
2.1. Overview of Onset of EMG Movement-related Events Detection Methods
In this section three EMG event detection approaches will be discussed, namely the
threshold-based methods, the denoising pre-processing for threshold-based methods, and the
model-based methods.
2.1.1. Threshold-based Methods
The most frequently used methods are those that employ some form of a threshold level
detection. Their principle is that when the signal exceeds a predefined threshold level the
detection method signals the movement onset. Threshold-based methods are commonly applied
to the rectified EMG, and the threshold is defined either as a percentage of the EMG signal value
(Morey-Klapsing et. al., 2004) or as a sum of the mean and a multiple of standard deviations of
the EMG signal recorded prior to the onset of the muscle activity (Staude et. al., 2001, van
Boxtel et. al., 1993). Standard deviation is proportional to the number of active motor units and
the rate of activation (Clancy et. al., 2002), thus it is a useful value to define the threshold for
muscle activity onset. The performance of threshold-based methods depends on the quality of the
recorded EMG signal and signal-to-noise ratio (SNR). It is also affected by the crosstalk and
movement artefacts (Allison, 2003). There are two types of threshold-based detection methods:
a) single threshold and b) double threshold. Single threshold methods require for the EMG signal
values to exceed the set threshold to claim movement onset, while the double threshold methods
require the signal amplitude not only to exceed the threshold but also to remain above the
threshold level for a certain duration of time (Stokes et. al., 2000). Double threshold methods are
more robust than single threshold methods.
8
Multiple threshold-based methods have been proposed to date: 1) Greeley’s method
(Greeley, 1984), 2) Lidierth’s method (Lidierth, 1986), 3) Hodges and Bui’s method (Hodges et.
al., 1996), 4) Bonato’s method (Bonato et. al., 1998), and 5) Abbink’s method (Abbink et. al.,
1998). Greeley’s method detects the EMG movement-related event if several successive points
of the rectified EMG exceed the threshold level (Greeley, 1984). Lidierth defines such an event
similarly to Greeley’s method, but has an additional criterion that values of the EMG signal
should exceed the threshold level for at least T1 samples, and the drops below the threshold
within these T1 samples should not be longer than T2 samples (Lidierth, 1986). In Hodges’
method the event is identified if the mean value of the rectified and low-pass filtered EMG signal
within a sliding window exceeds the predefined threshold level (Hodges et. al., 1996). Bonato et.
al.’s method applies a whitening filter to the signal followed by data squaring instead of
rectification for pre-processing. It then computes the ratio between the sum of two successive
squared signal samples and the variance of the baseline level of EMG signal. Baseline level is
computed from first M samples of the signal and the ratio is computed only for odd time instants
of the signal (1, 3, 5, etc). If this ratio exceeds a certain level for at least n out of m successive
samples, this is called an active state, and if the active state persists for T1 samples, then the time
instant when the active state was first detected is the EMG onset (Bonato et. al., 1998). Abbink
used rectification and low-pass filtering as pre-processing, similar to Hodges, however, he used a
test function to search for a movement onset. This function takes signal point as an onset
candidate, and examines N samples prior to that point and N samples after the point. It counts the
amount of samples with values whose normalized amplitudes are below the threshold among the
N preceding samples and the amount of samples whose normalized amplitudes are above the
threshold among the N following samples. The onset is defined as the location where the sum of
these computed numbers is maximal (Abbink, 1998).
2.1.2. Denoising
When the EMG signal is very noisy, i.e., SNR is low, the direct application of thresholding
to the EMG signal may fail to detect movement onset. To address this problem Donoho proposed
an algorithm that applies wavelet-based processing which can be used to suppress the noise
levels within the signal before detection is performed (Donoho, 1995). Donoho’s denoising
approach consists of three steps: 1) computing wavelet coefficients of the noise; 2) applying soft-
9
thresholding non-linearity to the entire signal; and 3) reconstructing the signal. In the first step,
the data representing the noise has to be decomposed into several sequences of coefficients. For
each sequence of coefficients, the average of the coefficient values is removed and the variance
is calculated. The variance is used as the threshold for the next step. In the second step, the data
representing the sum of signal and noise is decomposed under the same conditions as the noise
data. The noise variances calculated in the first step are now subtracted from the sequences of
coefficients representing the sum of signal and noise. If the resulting difference was greater than
zero, the difference was kept; otherwise, the sequences of coefficients were assigned to zero.
This step removes the effect of noise but retains the signal properties. In the last step, the
modified sequences of coefficients are used to reconstruct an estimate of the signal without noise
(Sin, 2007). The detection by the threshold-based method is frequently easier from such denoised
signals; therefore, Donoho’s denoising can be a valuable pre-processing step before the
application of threshold-based detection, such as those described in Subsection 2.1.1.
2.1.3. Model-based Methods
Several EMG movement-related events detection techniques are based on maximum
likelihood tests (Stylianou et. al., 2003, Staude et. al., 1999, Staude et. al., 1995). These methods
require the use of adaptive whitening filters to turn an EMG signal into a Gaussian random
process, so that its properties could be described by Gaussian probability density function. Then
the detector, called optimal estimator or EstOpt by the authors, compares the probability
distributions of the signal before and after every hypothetical onset point, which depend on the
known EMG signal variance profiles. The variance profile before the hypothetical onset point
corresponds to the baseline activity and the one after the onset point to the activity during muscle
contraction. The test is done by computing a log-likelihood ratio between these probability
distributions and comparing it to a threshold. If this ratio’s maximum value among all possible
hypothetical onset points exceeds a threshold, then the point where this maximum value occurs is
defined as the onset (Staude et. al., 1999).
When variance profiles are not exactly known, they can be estimated by a set of parameters.
Staude et. al. proposed using an Approximated Generalized Likelihood Ratio (AGLR) detector
with two after-change variance profiles models: 1) step-like profile, i.e. constant variance after
the onset, different from the one before the onset; or 2) ramp-like profile, i.e. variance after the
10
onset has a constant term and an additive change term. The unknown variance profile before the
onset is estimated as the average signal energy of the first M points of the signal. A sliding
window of fixed size W moves along the data and for every window’s position the parameters in
the after-change variance profile are estimated from the points within the window and log-
likelihood ratio test is set up based on the estimates. Detailed implementation of the algorithm is
available in Staude et. al., 1995, Staude et. al., 2001.
Model-based methods of detecting EMG movement-related events can be viewed as the
examples of application of parametric change-point analysis. A review of this type of analysis
and its common techniques is presented in the following Section 2.2.
2.2. Overview of Change-point Analysis Methods
In this section common change-point analysis methods are described.
2.2.1. Concepts, Definitions, Applications
Mathematical statistics methods are commonly used for data modeling and analysis. Most of
statistical analysis of data requires making an assumption that there is a unique probabilistic data
generation mechanism (DGM, also known as data generation process or DGP). However, in
complex systems frequently this mechanism can change in time or in phase space, therefore, it
may be necessary to properly analyze such data to subdivide it into the segments with different
DGM’s. The relatively new field of statistics, called statistical diagnosis, addresses the problem
of figuring out if there is more than one DGM that gives rise to the data. The main problem of
statistical diagnosis, investigated actively since 1950s, is a so-called change-point problem, a
task of detection of abrupt changes in the probabilistic characteristics of the data that happen at
the unknown instants (Brodsky et. al., 2000, Basseville et. al., 1993).
There are several classifications of statistical diagnosis problems. For example, there is
retrospective analysis of the data when the data is analyzed after the data collection was
complete, and there is sequential analysis when the data is analyzed as the data collection is
ongoing. There is also a classification based on the assumptions made about the data. There are
parametric methods of change-point detection in which a probabilistic model of the data
generation is known and is used to find the location of the change, There are also nonparametric
11
methods which do not use any a priori information on the probabilistic structure of the data
(Brodsky et. al., 2000).
Change-point analysis has been applied to analyze the time series in different fields such as
process control (Page, 1954), climate studies (Vautard et. al., 1989), econometrics (Chen et. al.,
1997), EEG analysis (Cassidy, 2002; Kaplan et. al., 1999, Kaplan et. al., 2005) and
demographics (Denison et. al., 2001).
2.2.2. Methods of Change-point Analysis
A single change-point problem was defined by E.S. Page in mid 1950s (Page, 1954; Page
1955; Page 1957) who investigated the problem of quality control in a continuous production.
Page proposed a change-point problem formulation as follows: a sequence of observed random
variables x1, x2, …, xN has some change of parameter occurring at an unknown point m, and the
original value of parameter before the change is known to be θ. Page suggested computing
cumulative sums: ∑=
−=r
iir
xS1
)( θ , S0=0, and announcing a change when
hSSi
rir
≥−<≤
min0
, i.e. when the current cumulative sum exceed the minimum cumulative
sum by a specified amount h (Page, 1955). Since the work by Page other approaches for change-
point detection in independent random sequences were proposed: Bayesian approach by
Chernoff and Zacks (Chernoff et. al., 1964) and maximum likelihood test by Hinkley (Hinkley,
1971).
Taylor proposed a valuable method of change-point detection (Taylor, 2000). He proposed
the use of cumulative sum technique and bootstrapping. Cumulative sum (CUSUM) charts are
the same as those proposed by Page (Page, 1955) and Hinkley (Hinkley, 1971) where the mean
of the signal is used as the parameter. The bootstrapping procedure requires constructing
numerous (1000-10,000 or more) CUSUM charts using the reordered data. One can compute the
difference between the maximum and minimum of the CUSUM chart and use this number for
comparison of the chart based on original data to those based on reordered data. This difference
in the original chart should be bigger than that in 95% of rearranged data charts in order to be
significant. If it is indeed significant, then the change is declared where the maximum of the
absolute value of the original CUSUM chart occurs. After the change has been detected, the data
12
can be broken up into two pieces before and after the change-point, and analysis can be repeated
to seek other change-points (Taylor, 2000).
The first nonparametric method of change-point detection was proposed by Bhattacharya
and Frierson (Bhattacharya et. al., 1981). They proposed a statistic similar to that of Bayesian
change-point detection by Chernoff and Zacks, but used ranks rather than values of observations.
Brodsky and Darkhovsky proposed the use of Kolmogorov-Smirnov statistics (Equation 1),
commonly used for checking the equality of distributions, for the detection of both single and
multiple change-points.
Equation 1: Kolmogorov-Smirnov detection statistic
−−
−= ∑∑
+==
N
nk
Nn
k
N
Nkx
nNkx
nN
n
N
nnY
11
)(1
)(1
1),(
δ
δ
for 10 ≤≤ δ , 11 −≤≤ Nn where xN is a diagnostic sequence for the signal, δ is a false
alarm probability. Diagnostic sequence is some sort of function computable from the original
random sequence to convert the problem into the detection of changes in mean value. The
diagnostic sequence is assumed to have the form of a step function of time and random noise.
The statistics YN is computed for the diagnostic sequence, and the maximum of its absolute value
is determined. If this maximum is greater than a threshold determined from the data, then the
location of this maximum is assumed to be a change-point. To search for more change-points, a
sequence can be subdivided into two segments before and after the found change-point, and the
process repeated on these pieces until no new change-points are located (Brodsky, et. al., 2000;
Brodsky et. al., 1999).
Some researchers presented methods of change-point analysis that depend on subspace
identification. Such methods have an advantage over the parametric methods that they do not
require any apriori parameterizations, therefore, one does not have to make any assumptions
about the probability distributions of the data. The main approaches are singular spectrum
analysis (SSA) based method (Goljandina et. al., 2001; Moskvina et. al., 2003) and state-space
model (SSM) based method (Kawahara et. al., 2007).
The SSM method is a more recent and more general approach to the problem of change-
point detection using subspace identification. It uses generic SSMs as the model for the time-
series, so it can handle more abundant types of time series data. SSM method assumes the signal
13
y(t), t=1,2… to come from a linear state-space system:
+=
+=+
)()()(
)()()1(
twtCxty
tvtAxtx, where x is
a state vector, y is a system’s output, and v and w are the system and observation noises
respectively. The SSM-based method requires estimation of the column space of the extended
observability matrix [ ]TkTT
kCACACO )()( 1−= L from the signal’s reference
interval by numerical methods, including LQ decomposition of a matrix (decomposition into a
product of a lower-triangular matrix L and orthogonal matrix Q (Nicholson, 2003)), matrix
square root calculations, and singular value decomposition. Then a distance between the
subspace of this observability matrix and the Hankel matrix based on the test interval is
calculated, and its increase can serve as an indicator of change (Kawahara et. al., 2007). Its
disadvantage is the bulky computation and the need for recursive processing.
The SSA-based method is an older and more classical subspace identification algorithm.
Although it is less general than the SSM method, because it attempts fitting autoregressive model
to the segments of the time series, it involves simpler signal processing. SSA-based method
performs the principal component decomposition of the “trajectory” matrix based on the Takens’
embedding (Takens, 1981) of the original time series, and then analyzes the series using these
components. Unlike the SSM algorithm, only singular value decomposition of matrices is needed
to compute the approximation for a subspace. If the generating mechanism for the series changes
at some point, then there is an increase of a distance between the vectors of the trajectory matrix
based on the signal after the change-point and the components computed from the signal before
the change-point. This is a property that allows detecting the changes in the signal. (Goljandina
et. al., 2001; Moskvina et. al., 2003). The detailed explanation of SSA and SSA-based change-
point detection algorithms is presented in Section 2.3.
2.2.3. Review of Change-point Analysis Applications to Biological Signals
The techniques of change-point analysis are not yet frequently applied to the problems in
biology. However, several significant applications have already been established. One
application is the EEG segmentation (Wendling et. al., 1997; Brodsky et. al., 1999; Kaplan et.
al., 2005). Wendling et. al. analyzed the EEG segments recorded from patients with epilepsy in
an attempt to detect regions of stable neuronal activity during seizures and to compare different
14
algorithms for signal segmentation. They applied two parametric CUSUM-based algorithms and
two nonparametric methods detecting frequency changes. They studied dependence of different
algorithms on type of change, performance on simulated and real signals and ability of the
algorithms to obtain the instant of change (Wendling et. al., 1997).
Kaplan’s group at Moscow State University used the change-point analysis to subdivide
EEG signals into stationary segments. They viewed each homogenous segment of the EEG
signal as a period of stable activity of some group of neurons; and the transitions from one
segment to another as the moments of the change in the electrical activity of this group of
neurons or switching to a different group (Brodsky et al. 1999). Kaplan et. al. used the change-
point detection technique developed by Brodsky and Darkhovsky, in which EEG signal’s power
was used as a diagnostic function. Kaplan et. al. successfully demonstrated the detection of
changes in EEG’s alpha band (7.5-12.5 Hz) in their early papers (Brodsky et. al., 1999, Kaplan
et. al., 2000). They also presented an approach to study the nonstationary nature of EEG signals
by means of segmentation of EEG signal into stationary pieces, characterizing them by their
properties and studying the coincidence level between switching moments among different
channels (Kaplan et. al., 2005).
Brown et. al. applied the change-point analysis to analyze changes in the spectra of signals
recorded from the subthalamic nuclei (STN) of patients with Parkinson’s disease (Cassidy et. al.,
2002). Oscillation model of the basal ganglia (a group of nuclei in the brain participating in
movement control) predicts that beta band (frequencies from 11-30 Hz) in the STN is antikinetic,
i.e., it opposes movement, while gamma band (>60Hz) is prokinetic, i.e., promotes movement
(Hutchison et. al., 2004; Brown, 2003). Therefore, this model suggests that the power of the
signal in the beta band will decrease due to movement, while the power of the signal in the
gamma band will increase due to movement. This is what Brown et. al. tested by means of
change-point analysis. They recorded the activity of the STN in selected patients who were
performing simple motor task after being prompted to do so by an external command. They
filtered STN recordings in beta and gamma bands and applied the detection method developed
by Taylor (Taylor, 2000) based on the CUSUMs and bootstrapping. They were able to show
successfully that movement causes the changes in the spectra. In particular, they detected
suppression of the power at 20Hz and increase of power at 70Hz during the time the patient was
moving.
Parametric methods of change-point detection, based on maximum-likelihood approach, were
applied by Staude and Wolf to EMG events detection and studies of motor control in humans
15
(Staude et. al., 1995; Staude et. al., 1999). Their algorithms were briefly outlined in Subsection
2.1.3. While their study produced valuable detection methods, they were designed for the EMG
signals modeled as the white noise process with the time-varying mean serving as an input to an
autoregressive (AR) process with constant known coefficients, rather than the experimentally
recorded EMG signal. Secondly, because they used the parametric change-point detection
methods, they had to transform the simulated EMG signal into a sequence of “innovations” that
would reflect the deviations from the baseline signal due to muscle activation and would have a
Gaussian distribution, so that they could be used in a log-likelihood test. Thus, the adaptive
whitening filter had to be designed to compute the “innovations sequence” with the coefficients
depending on the simulated EMG signal’s AR parameters (Staude et. al., 2000). It, however, may
be a nontrivial task to compute these coefficients for a recorded signal. For this reason a
nonparametric change-point analysis method applicable to the EMG onset detection problem
would be an asset, since for a nonparametric method there are no assumptions about the
probability distribution of the signal being made.
2.3. Singular Spectrum Analysis (SSA) and Change-point Detection
In this section SSA signal processing approach and SSA-based change-point detection
method are discussed.
2.3.1. SSA Theory and Applications
SSA is a reasonably well-known signal processing technique. It was developed in the 1980s
by Broomhead and King (Broomhead et. al., 1986). Since then it has been applied to analyze
meteorological, climatic and geophysical time series (Vautard et. al., 1989; Vautard et. al.,
1992). The SSA algorithm described according to (Goljandina et. al., 2001) involves four main
steps:
1) Construction of the trajectory matrix by the Takens’ embedding of the original time
series with a desired lag (Takens, 1981). Let x1,x2,…xN be a time series, and choose lag
parameter M. Set K=N-M+1. Then the trajectory matrix is defined as Equation 2.
16
Equation 2: Trajectory matrix for Singular Spectrum Analysis
=
+
+
NMM
K
K
xxx
xxx
xxx
X
L
MOMM
L
L
1
132
21
(Goljandina et. al., 2001; Moskvina, et. al.,
2003)
2) Computation of a Singular Value Decomposition (SVD) on the trajectory matrix. This
can be done directly, or by first computing the lag-covariance matrix R=X*XT and
determining its eigenvalues λi and eigenvectors Ui of R ( ],1[ Mi ∈ ). Then the principal
components vectors Vi, which correspond to the eigenvectors of the matrix XT*X, can be
computed as:
i
i
T
i
UXV
λ= . From λi, Ui and Vi one can compute the decomposition
X=X1+X2+…+XM, where T
iiiiVUX λ= (Goljandina et. al., 2001; Moskvina et. al.
2003).
3) Grouping of the components. One can select groups of components depending on the
signal processing task being performed, for example, for denoising, one can group the
components corresponding to the signal and components that correspond to noise.
4) Reconstruction of the signal based on selected components. According to the grouping,
one computes the matrix sum for groups of Xi (size M by K). Define M*=min (M, K) and
K*=max(M, K), x*ij=xij if M<K and x*ij=xij otherwise. Then the series g0, …, gN-1 can be
computed as Equation 3:
Equation 3: Reconstruction of Signal after SSA-decomposition into components.
<≤−
<≤−
−<≤+
=
∑
∑
∑
+−
+−=
+−
=
+−
+
=
+−
NkforKxkN
KkforMxM
Mkforxk
g
KN
Kkm
mkm
M
m
mkm
k
m
mkm
k
*1
2
2,*
**
1
2,*
*
*1
1
2,*
*
*
*
1
11
101
1
(Goljandina et. al.)
This corresponds to averaging entries of Xi that are located on the diagonals i+j=const.
17
Applications of SSA include, for example, denoising, detection or removal of the trends,
selection or exclusion of periodic components, as well as filtering, smoothing and forecasting
(approximating missing values) for the signals (Goljandina et. al., 2001).
The assumption of the SSA is that the time series, to which SSA is applied, can be well
approximated by linear recurrence formula (LRF), i.e. the series xt=zt+et where zt is a solution of
d-td1-t1tzazaz +…+= of order d with coefficients a1, .., ad and et is some noise that cannot
be well approximated by the finite-difference equations. The process zt has a form of Equation 4:
Equation 4: Form of the process, which can be well represented by linear recurrent formula
∑ +=k
kk
t
kttetz k )2sin()( φπωα µ
,
where αk(t) are polynomials in t, µk,ωk and φk are parameters. zt with up to M non-zero terms
should be a reasonable approximation of the signal to which SSA is applied. SSA does not
assume any parametric model or any structure, such as stationarity, instead it attempts to
generate this model from the signal. (Moskvina et. al., 2003).
2.3.2. Change-point Detection Algorithm Based on SSA
The algorithm to detect the change-points in the data using SSA was developed by Moskvina
and Zhigljavsky at Cardiff University, UK. The idea behind the algorithm is to apply SSA to a
windowed portion of the signal. SSA picks up a structure of the windowed portion of the signal
as an l-dimensional subspace.
If the signal structure does not change further along the signal, then the vectors of the
trajectory matrix further along will stay close to this subspace. However, if the structure changes
further along, it will not be well described by the computed subspace, and the distance of
trajectory matrix vectors to it will increase. This increase will signal the change.
The following is the description of mathematics involved in change-point detection
algorithm:
Let x1,x2,…xN are a time series, N is large. Choose window width m and the lag parameter M,
such that M≤m/2. Set K=m-M+1. Then for each n=0,1,…,N-m-M take an interval of time series
[n+1, n+m] and define the trajectory matrix Xn, size M by K (Equation 5)
18
Equation 5: Equation of the trajectory matrix for SSA-based change-point detection.
=
++++
++++
+++
mnMnMn
Knnn
Knnn
n
xxx
xxx
xxx
X
L
MOMM
L
L
1
132
21
For each n=0,1,…N-m-M
1) Compute lag-covariance matrix (Equation 6)
Equation 6: Equation of the lag-covariance matrix for SSA-based change-point detection.
Rn=Xn*XnT
2) Determine M eigenvalues and eigenvectors of Rn and sort the eigenvalues in decreasing
order.
3) Compute the sum of eigenvalues and the percentage of this sum that each eigenvalue
contributes. The greater this percentage the more important is the component
corresponding to the eigenvalue.
4) Select the number of components to use for change-point detection.
For change-point analysis, it was found that it works best to select a group of components
that represent most of the signal. The number of components in this group is defined as L,
and the choice of L remains fixed for all the Xn computed from the signal.
5) One has to pick two parameters of test interval p and q (both greater than 0) and define a
test matrix T on an interval [n+p+1, n+q+M-1] (Equation 7)
Equation 7: Equation of the test matrix for SSA-based change-point detection.
=
−++++++++++
++++++++
+++++++
111
1432
321
MqnMpnMpnMpn
qnpnpnpn
qnpnpnpn
n
xxxx
xxxx
xxxx
T
L
MOMMM
L
L
The only requirement is that the interval defined by the choice of p and q allows forming
a test matrix that includes at least one column of signal values different from the
trajectory matrix columns.
6) Compute Dn(Tn) statistic, the sum of squared Euclidean distances between the vectors of
the test matrix T and L chosen eigenvectors of the lag-covariance matrix Rn (Equation 8).
19
Equation 8: Equation for Dn statistic
( ) ( )( )∑+=
−=q
pj
n
j
TTn
j
n
j
Tn
jnTUUTTTD
1
)()()()(
where Tj(n)
are the vectors constituting the test matrix Tn, and U is a matrix consisting of
L eigenvectors of Rn. The increase of the value of this statistic signals that the change has
occurred.
The first way to estimate the change-point locations is to compute local minima of the
Dn(Tn) function preceding its large values.
7) To find precise locations of change-points an additional CUSUM statistic calculation is
needed. CUSUM statistic is computed for n=0…N-m-M (Equation 9):
Equation 9: Equation for CUSUM statistic.
( )[ ])(3/1,0max
,
11
00
pqMSSWW
SW
nnnn−−−+=
=
++
(Moskvina et. al., 2003, Moskvina, 2001),
where Sn= Dn/vn, vn is an estimator of the normalized sum of squared distances Dn at time
intervals, at which the hypothesis of no change can be accepted. vn is effectively a variance
of noise in the signal. (Moskvina et. al., 2003)
If Wn exceeds a threshold (Equation 10)
Equation 10: Equation of the threshold for changes in SSA-based change-point detection
)1)(*3(*3
2
)(1 2
MpqMMpqM
th −+−
−+= α
,
where tα is a (1-α) quantile of the standard normal distribution, then the change-point
estimate is a first point with non-zero value of Wn before reaching this threshold (Moskvina,
2001).
2.3.3. Why Choose the SSA-based Algorithm for this Study?
The SSA-based algorithm was selected as the candidate change-point detection method for
several reasons. Firstly, its implementation is rather straightforward since it is based on very
standard time-series analysis techniques such as embedding and singular value decomposition
commonly used in, for example, sensor array signal processing applications (Manolakis et. al.,
20
2005). Fewer complicated matrix manipulations are needed than in the SSM algorithm, for
example, LQ factorizations (Nicholson, 2003) and matrix square root computations are not
required for the SSA-based algorithm. Secondly, Staude et. al. showed that LRF models are
reasonable to model EMG signals with (Staude et. al., 1999, 2000), thus, SSA should be able to
give good results when computing EMG signals structures for the segments of EMG signals
within the moving window of the SSA-based algorithm.
2.4. Summary of the Chapter
At the beginning of this chapter the review of commonly used EMG event detection methods
was presented. Several common threshold-based algorithms (Greeley, Hodges, Lidierth, Bonato,
and Abbink) and two model-based algorithms for muscle activation detection were briefly
outlined. The concept of wavelet-based denoising was also described. The second portion of this
chapter was devoted to change-point analysis. Firstly, the main concepts and definitions were
given, then common techniques were summarized and the singular spectrum analysis change-
point detection algorithm is presented in detail. Some existing applications of change-point
analysis to biological problems were introduced at the end of the chapter.
21
Chapter 3: Objectives and Hypothesis
3.1. Objectives
The objective of the project was to investigate an application of the nonparametric change-
point detection method based on the subspace identification to the problem of finding the
movement-related events in raw EMG signals with different levels of baseline activity. The
comparison of such a method to two conventional threshold-based detection methods as well as
to visual event onset detection had to be performed. Wrist EMG signals with and without tremor
and trunk EMG signals were chosen for this application of change-point analysis.
The choice of wrist EMG with tremor and trunk EMG signals was made with the purpose of
giving a more challenging task to the algorithm. It was expected that the algorithm would
perform well with clean wrist EMG signals. More complicated signals were chosen for analysis
to better understand what the algorithm’s abilities are. Wrist EMG with tremor provided the
challenge of multiple large changes present in the signal and trunk EMG had much higher noise
levels than wrist signals and also contained multiple changes.
3.2. Hypothesis
The SSA-based algorithm computes the detection statistics which, if they exceed a certain
threshold, signal a significant change. However, it is likely that there will be multiple changes
detected in the signal. One possible way to decide which changes are most important is based on
the relative height of peaks corresponding to the changes in the detection statistics. The
hypothesis of the project to be tested was that the largest change in the EMG signal detected by
the SSA-based change-point detection algorithm corresponded closely to the movement-related
muscle activation.
22
Chapter 4: Methods
In this chapter the overview of EMG data collection, detailed description of employed
algorithms, their MATLAB implementations and parameter selection will be described. Overall
signal processing set-up and subsequent detection results analysis will also be outlined.
4.1. Data Acquisition
In this section data acquisition experiments used to acquire EMG data are presented.
4.1.1. Wrist Extension Experiments
At the Toronto Western Hospital nine individuals with Parkinson’s disease were invited to
participate in wrist extension experiments during which EMG was recorded from extensor carpi
radialis muscles, using Meditrace surface electrodes, placed ~3cm apart over the skin overlying
these muscles. The ground electrode was placed on the bone, to the medial side of the wrist. The
location of electrodes is shown in Figure 1. Skin was prepared with alcohol wipes prior to
electrodes placement. The SynAmp amplifiers (NeuroScan Laboratories, USA) were used to
amplify raw EMG signals. The sampling rate of the data acquisition system was 1 kHz. EMG
filters were set at 30-500 Hz.
23
Figure 1: Diagram showing electrodes locations for recording of EMG from extensor carpi radialis muscles.
Rectangle is the location for recording electrodes and circle is a place of reference electrode. Provided by Dr.
D. Sayenko, 2008.
Participants were seated in an armchair in front of a computer monitor. First the EMG
activity was recorded at rest for 1-2 minutes. Then participants were asked to perform wrist
extension tasks followed by passive wrist flexions (i.e., the hand dropped due to gravity after the
extension was completed) with one arm/hand. They were asked to perform two types of tasks:
• Internally triggered task (i.e., a participant decided when to initiate a movement) where
participants had to perform wrist extensions every 5-10s. The sequence of movements
was self-paced. Typical duration of internally triggered tasks was between 10 and 15
minutes.
• Externally triggered task (i.e., the task was initiated after a prompt was given) where
participants had to perform wrist extensions when the computer monitor flashed green.
The externally triggered tasks were recorded until about 40 wrist extensions were
performed (this took between 4 and 7 minutes).
Both externally and internally triggered tasks were first performed by the participants after
the overnight withdrawal of dopamine medication, then the usual dose of medication was
administered and both tasks were performed again (Paradiso et. al., 2003).
24
4.1.2. Trunk Muscles Involved in Sitting
The EMG data from the trunk muscles was collected by Vivian Sin, a graduate student in
Rehabilitation Engineering Laboratory. The following description of the data acquisition is based
on Vivian’s M.A.Sc. thesis (Sin, 2007).
Thirteen healthy, able-bodied male subjects participated in the perturbed sitting study. They
were asked to sit on a special apparatus and to wear a custom-made harness. This harness,
approximately 12cm wide and 1.35m long, was made of canvas, with loops approximately every
3 cm apart, and secured by velcro and fasteners. External perturbations were applied manually in
different directions by a researcher using a rope in series with a force transducer to the harness.
Eight ropes of about 1m length were attached to the loops of the harness at equal intervals by
means of biners; force transducer could be connected by means of another set of biners to the
free ends of the desired ropes. The perturbation directions were labeled as 1 to 8, with direction 1
corresponding to the anterior direction, and incrementing clockwise by 45 degrees as shown in
Figure 2.
Figure 2: Directions of perturbation (Sin, 2007)
There were a total of 40 perturbation trials (8 directions, 5 times each). The perturbation trials
were given in random order such that the subject was not pulled consecutively in the same
direction to prevent fatigue and anticipation.
During each perturbation, surface EMG measurements were recorded using disposable silver-
silver chloride surface EMG electrodes with a diameter of 10mm and a distance of 18mm
between them. Each electrode was connected to a preamplifier before connecting to the Bortec
AMT-8 EMG system. The EMG system had a frequency response of 10 to 1000Hz for each
channel, and a common mode rejection ratio of 115dB at 60Hz. Two EMG systems were used
during the experiments for a total of 16 channels of EMG recording. The EMG signals were
sampled at 2 kHz.
25
Surface electrodes were placed bilaterally on the skin above the following muscles: rectus
abdominis (RA) - 3cm lateral to umbilicus, aligned vertically; external obliques (EO) -
15cm lateral to umbilicus, aligned 45 degrees to the vertical, internal obliques (IO) – midway
between ASIS and symphasis pubis, above the inguinal ligament, aligned 45o to the vertical;
thoracic erector spinae (T9) – 5cm lateral to the T9 spinous process, aligned vertically; lumbar
erector spinae (L3) – 3cm lateral to L3 spinous process, aligned vertically; latissimus dorsi (LD)
– lateral to T9 spinous process, over the muscle belly; sternocleidomastoid (SM) – 1/3 the
distance from the sternal notch to the mastoid process at the distal end overlying the muscle
belly; and splenius capitis (SC) – over the C4-C5 level, aligned vertically. The reference ground
was placed over the clavicle. Figure 3 shows the locations of the surface EMG electrodes (Sin,
2007).
Figure 3: Front view (left) and back view (right) of the locations of EMG electrodes for trunk muscles EMG
recordings (Sin, 2007)
4.2. SSA-based Change-point Detection Algorithm Parameters Selection and
Implementation
4.2.1. Parameter Selection
26
To run the change-point detection algorithm, a choice of five parameters had to be made: lag
parameter M, sliding window length m, the number of components used to perform change-point
detection L, and parameters p and q defining the test interval (and test matrix).
a) Selecting lag M and window size m: Tests with Gaussian noise
Lag M is a very important parameter, since it relates to the number of non-zero terms in the
LRF that SSA tries to compute from the signal, to pick up its structure. If the signal is highly
complex, then embedding it with a small lag will not allow obtaining enough components to
have an accurate representation of the signal (Goljandina et. al., 2001, Moskvina et. al., 2003).
The choice of lag is also associated with tuning to a particular signal’s frequency; however,
because a signal might not have some dominant frequency and instead may have time-varying
frequency having a fixed lag might not give suitable change-point detection results. On the other
hand, M cannot be picked to be too large due to the computational constraints, such as
computing the singular value decomposition for large matrices.
Another parameter is a window size. On one hand it should be big enough to allow capturing
enough of a signal structure to use for the change-point detection, on the other hand, if it is too
big then small changes in the signal may be undetected. If the window is too small, then signal
outlier values may be taken as characteristic of the signal, and thus many false change-points will
be detected (Moskvina et. al., 2003). The choice of lag M constraints partially the choice for the
window size m, since m has to be at least twice greater than M.
Several simple tests were done with the 10000 points-long random Gaussian noise signal
with mean 0 and variance 1. Change-point analysis functions have been run on this noise, with
the expectation to find no changes. Different selections of lag parameter were made and window
size was picked to be twice the lag. It was observed that picking a bigger lag (M=100), allows
the more accurate (although a very slow) detection of changes, while small lag (M=25) made the
detection statistic highly erratic, detecting many outliers as changes, while lag of M=50 seemed
like a reasonable trade-off between computation time and detection accuracy, although it made
several false detections. For this reason a value of M=50 and a corresponding value of m=100,
were chosen for the change-point detection in EMG signals. Results for the detection of change
in Gaussian noise are shown in the Figure 4.
27
Gaussian Noise mean 0 var 1
-5
-4
-3
-2
-1
0
1
2
3
4
5
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
n
(a)
CUSUM statistic M100 m200
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
n
(b)
CUSUM statistic M50 m100
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
n
(c)
CUSUM statistic M=25, m=50
-0.5
0
0.5
1
1.5
2
2.5
3
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
n
(d) Figure 4: Test of effect of lag parameter on change-point detection in Gaussian noise (a) Gaussian noise,
10,000 points, mean 0, var 1, (b-d) Results of change-point detection with (b) lag M=100, m=200, (c) M=50,
m=100, (d) M=25, m=50. Blue line is detection statistic, pink line shows the threshold. Notably, plot (b) shows
less false changes detected than plots (c) and (d), thus showing increase of accuracy with lag parameter.
28
b) Selection of the number of components L
If more components L are included in the change-point detection process then we take in
some noise in the change-point detection thus obscuring the changes, while if the number of
components used is not sufficient, then the relevant changes may actually be occurring in the
overlooked components. A reasonable approach to choosing L is taking the most important
components judging from their corresponding eigenvalues. There are a couple of possibilities.
Firstly, one can take components of the signal so that the sum of the eigenvalues of selected
components exceeds a certain amount of the total sum (say, 80% or 90%). Another way is taking
all components whose eigenvalues exceed 5% of the sum of eigenvalues. By performing the
SSA-based reconstructions of the signal from the components, it was observed that the
components whose eigenvalues were less than 5% of the sum’s value yielded noise-like time
series, rather than signal-related ones, therefore, they could be commonly ignored. This latter
approach was implemented.
Because there are N-m-M+1 matrices being evaluated, each of them may have a different
value of L based on the above criterion. To pick a single value of L, a couple of things can be
done. One possibility is to compute the values of L for all n and take the most frequently
occurring value. Another way is to take L based on a trajectory matrix at the beginning of the
signal, i.e. computed for n=0. This is reasonable because one can assume that there is no change
occurring at the very beginning of the signal. This is also consistent with an algorithm
description suggested in Moskvina Ph.D. thesis (Moskvina, 2001).
c) Selection of test interval parameters p and q
The parameters p and q define a part of the signal following the window from which the
trajectory matrix was constructed and possibly partially overlapping with this window. In
choosing the values for p and q, q should be slightly larger than p, but not too large, in which
case the detection statistics will smooth out the changes. The recommended values for p and q
are p=K=m-M+1, and q=m+1, so that the difference q-p equals to M, because in this way, the
test interval uses M-1 points from the trajectory matrix interval and M new points to construct M
test vectors. But q-p does not have to equal M and other choices of p and q can be reasonable, for
29
example, (p,q)=(m,m+1) when M new points give only one test vector, or (p,q)=(m,m+M) when
2M-1 new points yield M test vectors (Moskvina et. al., 2003, Moskvina, 2001).
4.2.2. MATLAB Implementation
The algorithm for change-point detection described in Subsection 2.3.2 was implemented in
MATLAB software package (Mathworks Inc., USA). The code of this implementation is
attached in the Appendix A. The performance of the script has been compared against that of the
program ChangePoint created by the algorithm developers, which is available at
http://www.cf.ac.uk/maths/subsites/stats/changepoint/. The perfect match in the computation of
Dn statistic and a reasonable closeness in CUSUM statistics (peaks of the same shape detected at
the same positions in time, but having different overall magnitude) were achieved between
MATLAB implementation and algorithm authors’ program.
The steps 1, 3, 5, and 6 of the change-point detection algorithm in Subsection 2.3.2 were
implemented as described there.
Determination of L, the number of components to be used for decomposition labeled as step
4 of the algorithm, was actually performed prior to steps 1-3. The trajectory matrix X0 was
constructed and SSA-decomposed. L was defined as the number of components with eigenvalues
greater than 5% of the total sum of eigenvalues of the matrix X0X0T.
Actual SSA decomposition (step 2 of the algorithm) was implemented by means of the eig
command in MATLAB, which computes eigenvalues and eigenvectors of a square matrix. The
outputted eigenvalues are sorted in decreasing order and the outputted eigenvectors’ magnitudes
are equal to 1. Alternatively, an svd (singular value decomposition) command could be used
directly on the trajectory matrix Xn; this would produce matrices U and V, where U are the
eigenvectors of XXT and V are eigenvectors of X
TX, and the returned singular values are squares
of the eigenvalues. eig was preferred to svd because of the extra computation that svd involves
which was not needed for the purposes of change-point detection.
For the computation of the CUSUM statistic, it was recommended by algorithm authors to
use vn=Dk(Xk), where k is the largest value of j<n, so that the hypothesis of no change could be
accepted in the interval [j+1,j+m] (Moskvina, 2001). This, however, is somewhat ambiguous,
since we do not know precisely the part of the signal where the changes start occurring. We can
30
only expect that there should be no change at the very start of the signal. To implement the
CUSUM statistic, the following vn formula was used (Equation 11):
Equation 11: Equation for vn used in MATLAB implementation of the change-point detection algorithm.
vn =Dn(Xn) for n<m/2 and vn=Dm/2(Xm/2) for n>m/2
This assumes that there is no change for n<m/2 (for the first half of the first window). This may
be a reasonable assumption for the application of EMG onset detection since there is always at
least a short rest period before the muscle activity changes. In addition to that on the webpage
http://www.cf.ac.uk/maths/stats/changepoint/ referred to in (Moskvina et. al., 2003) in the
description of the algorithm it was mentioned that changes are to be announced when CUSUM
statistic Wn exceeds the threshold for n>m/2. Alternative formulae could also be used to evaluate
vn (Equations 12 and 13):
Equation 12: Alternative formula for vn calculation
vn=Dn(Xn) for all n
(this was proposed in the ChangePoint software Help Menu, however, upon implementation, the
CUSUM statistics computed by the ChangePoint software and by MATLAB script did not
match),
Equation 13: Alternative formula for vn calculation
∑−−
=−=
12/
0
)(2/
1 mn
innn
TDmn
v for n >m/2 (Moskvina, 2001)
The threshold calculation for the change-point detection was done differently from the
formula given in the algorithm description. In the Help menu for the ChangePoint software, an
alternative formula was proposed (Equation 14):
Equation 14: Alternative equation of threshold for changes in SSA-based change-point detection
)2(
8
−−=
pqMh .
The threshold in the MATLAB implementation was programmed as such to facilitate
comparison of outputs of MATLAB script and the ChangePoint program. For the actual
application of SSA-based change-point detection to EMG onset determination, the computed
CUSUM statistics were processed without using the explicit thresholds to define the predicted
onset location (see Subsection 4.4.1 for details).
4.3. Processing Set-up
31
This section describes how the change-point detection in the collected data was organized
and data analysis was performed.
4.3.1. Methods of EMG Movement-related Events Detection and Signal Pre-processing
The SSA-based change-point analysis method was applied to segments of EMG signals from
wrist extension muscles and trunk muscles. The datasets with the wrist EMG data were
subdivided into 6s or 6000 points long segments (sampling rate was 1kHz). Each of these
segments contained an EMG event. For the recordings of externally triggered activity, the
segments of signal were extracted from 3s before to 3s after the moment of the triggering.
Therefore, the actual muscle activation occurred between 3000 ms and 4000 ms in all segments.
For the internally triggered activity recordings, the crude onsets were computed first by applying
the Hodges and Bui algorithm for onsets detection in the entire recording, then 6s segments of
the signal were excised from 3.5s before the crude onset to 2.5 seconds after the crude onset.
This also ensures that the onset would occur between 3000 ms and 4000 ms in all segments. All
extracted wrist EMG segments were manually checked to ensure that there was no loss of EMG
signal, and that there was an increased activity due to movement, so that it made sense to
determine the movement onset in the segment. The datasets collected from the trunk muscles
involved in sitting were already subdivided into 4s or 8000 points long segments (sampling rate
was 2 kHz). The muscle activation event occurred about 1-1.5s after the start of many but not all
of these segments, because not all muscles had a reaction to perturbations in all directions. No
additional segmentation was required for these signals. Change-point detection method did not
require any additional processing of the signals prior to the application of the method.
The SSA-based method was applied as it was described in Section 4.2. However, instead of
computing the threshold and detecting the change-points in the final step, the algorithm stops at
computing the detection statistics Dn and CUSUM. The threshold for onset detection was not
used since it detects numerous small changes, most of which are not related to the movement
onset. Instead, a point was found where CUSUM statistic reached its maximum value, and then
one stepped backwards until the last value of CUSUM statistic preceding the maximum equaled
zero, which would be one of the change-points detected by the usual method with a threshold.
The onset was defined as the first (non-zero) point after the zero-valued point. The following
values of parameters were used: M=50, m=100, p=m-M+1=51, q=m+1=101, L depended on
32
each particular segment (with the determination process described in Subsection 4.2.2, but
ranged between 1 and 8. The window length m=100 was also a reasonable choice since main
frequencies of the EMG signal are in the range 30 to 200 Hz, so their corresponding periods are
at least twice shorter than the chosen window length, and thus are not affected by the windowing.
Several other known methods of onset detection were applied to the same EMG signal
segments for the purposes of comparing them to the change-point detection results. Firstly, three
specialists in EMG processing were asked to visually estimate the locations of movement onsets
in the signals. They were provided with a small MATLAB script plotting rectified EMG
segments on the full screen one after the other and allowing them to input their estimate of
muscle activation events by selecting the proper location with a cursor and clicking on this
location in the plot with a mouse to record the estimate change in the EMG signal (attached in
Appendix B). Secondly, the event detection was attempted using the Hodges&Bui threshold-
based algorithm (Hodges et. al., 1996). Thirdly, the same threshold-based algorithm was applied
on the EMG signal which was previously denoised using wavelet decomposition with Haar
wavelets (Donoho, 1995; Sin, 2007). The implementations of these algorithms in MATLAB are
attached in Appendices C and D.
Before the application of some of these methods, some additional signals processing was
needed. For visual detection and for Hodges&Bui algorithm application signals had to be filtered
with 30-200Hz bandpass filter and then rectified. Kaiser window FIR filters were used, and they
were applied in a zero-phase filtering manner, using a filtfilt MATLAB command, to ensure that
there is no phase shift in the filtered signals. Filters were generated using the Filter Design and
Analysis tool of MATLAB. For the wavelet-based method, signals were first rectified, then
wavelet decomposed, denoised and reconstructed, and following these operations Hodges&Bui
method was applied to detect the onset in the reconstructed denoised signal. The details on the
applications of these methods are discussed in the Subsections 4.3.2 and 4.3.3.
4.3.2. Application of Hodges&Bui Method
The Hodges and Bui algorithm used a sliding window corresponding to 50 ms of data (for 1
kHz sampling rate the window had 50 points and for 2kHz sampling rate it had 100 points). This
window was moved along the rectified EMG signal one sample at a time and the mean of values
within this window was computed. If the mean of the values of the signal in this window
33
exceeded the threshold, then the first point of the window was called the movement-related event
onset (Hodges et. al., 1996). The idea behind this windowing approach is to ensure that the EMG
activity was elevated over a sufficiently long time period, rather than just for a few samples, i.e.,
that it was associated with the muscle activity such as wrist extension.
To compute the threshold for the movement-related event detection for externally triggered
wrist movements, the section of the signal 500ms prior to the trigger event (i.e. between 2500
and 3000 ms of EMG segment) was subdivided into five 100ms portions. For each of these
portions a mean was computed and the median of five mean values was taken as the mean used
in the threshold computation. The standard deviation of the 100ms portion with the median mean
value was also used in this threshold calculation. The threshold was then defined as the mean
plus three standard deviations calculated above. The 50 ms window started from right after each
trigger event and was advanced by one sample for two seconds (2,000 samples) until the
movement-related event was found. After computing the movement-related event onsets, the
detected events were visually inspected to ensure that the calculated event locations were
reasonable.
For internally triggered wrist movements and trunk muscles a similar approach to the
threshold computation was used, except in the trunk EMG segments the region which was used
for threshold computation was between points 500 and 1500 (250 to 750 ms from the 4000ms
segment’s start) and in the internally triggered wrist EMG signals it was between 500 to 1000 ms
of the 6000ms segment. The 50ms window started sliding from the 1000ms time from the
beginning of the internally triggered wrist EMG segment and from the 750 ms time for the trunk
muscle EMG and was advanced by one sample until a movement-related event was found. After
the events were detected, they were visually checked to make sure that the calculated locations
made sense.
4.3.3. Application of Donoho’s Wavelet-based Denoising Method
The raw EMG signals were full-wave rectified. The first 500 milliseconds of each EMG data
were used to estimate the amount of noise in the signal. Each EMG signal was decomposed
using the Haar wavelets into 14 levels. The Haar wavelet is a function defined by Ψ(x) = Ф(2x) –
Ф(2x-1), where Ф(x) = 1, if 0 ≤ x < 1, and 0 elsewhere (Boggess et. al., 2001).
34
Haar wavelets were chosen because they were the simplest to use. According to the
recommendations of Vivian Sin’s MASc thesis (Sin, 2007), fourteen decomposition levels were
selected because it was the smallest number in which there was no distortion in the reconstructed
signal. When the number of decomposition levels was less than fourteen, a visible shift in the
average of the reconstructed signal was observed in the regions without EMG activity (Sin,
2007). This was observed for both trunk EMG data and wrist extension data.
After the denoising, Hodges&Bui method was applied to the denoised signals in the same
manner as described above to obtain the EMG movement-related events onset estimates. After
these onsets were determined, they were visually inspected to make sure that the calculated
locations made sense.
4.3.4. Comparison of Onset Detection Methods.
Several methods of comparison were applied to the signals. Firstly, a simple manual check
of all the EMG segments showed if the EMG movement-related event was detected or not by the
given method in a given segment. Secondly, for those datasets for which the experts’ visual
event onsets estimates were collected, it was possible to verify if the estimates of event onset by
change-point detection and by other methods fall within range of the visual estimates and
calculate how close they were to visual estimates, i.e. to assess the “quality of detection”. To do
this, the average absolute differences between the visual and computer estimates were computed
for a set of segments. Then the sets of these differences for different algorithms were compared
statistically. Details on the specific types of analysis are given in the Chapter 5 of the thesis.
4.4. Summary of the Chapter
In this chapter, in Section 4.1., the two experiments in which the EMG data was collected for
the analysis were described: data from the wrist flexion muscles (Subsection 4.1.1) and data from
trunk muscles (Subsection 4.1.2) involved in sitting. In Section 4.2. approaches to choosing the
parameters for running the SSA-based change-point detection algorithm (Subsection 4.2.1) and
details of MATLAB implementation of the algorithm (Subsection 4.2.2) were explained. In
Section 4.3., EMG signal processing approach that was used to compare the change-point
detection with the other methods was proposed (Subsection 4.3.4.). The segmentation of EMG
35
signals prior to change-point detection (Subsection 4.3.1) and the implementation of the
alternative methods for EMG event detection was described (Subsection 4.3.2 – 4.3.3).
36
Chapter 5: Results
In this chapter the results of the EMG events detection will be presented.
5.1. Sample Event Detection in Wrist and Trunk Muscle EMG
The typical movement-related event onset detection in the wrist muscle EMG is shown in
Figure 5.
0 1000 2000 3000 4000 5000 6000-500
0
500
n (ms)
Original EMG signal
EMG
onset
0 1000 2000 3000 4000 5000 60000
2
4
6x 10
4
n (ms)
Dn statistic
Dn
onset
0 1000 2000 3000 4000 5000 60000
500
1000
n (ms)
Cumulative sum statistic
CUSUM
onset
Figure 5: Sample detection results for wrist muscle EMG (a) Original EMG signal, (b) Dn detection statistic,
(c) CUSUM detection statistic. Red circle marks the computed EMG movement-related event onset.
Both detection statistics show low values for the portion of the signal when there is no
change and a large increase in their values when a change occurs due to muscle activation. After
the increased muscle activity is over, the detection statistics fall off to the low values again. The
37
event onset shown in the plots is computed from the CUSUM statistic. The time of the peak
value of this statistic for each EMG segment is taken and the first location where the statistic is
equal to zero preceding the peak time is searched for. This is the value defined as event onset.
The detection of movement-related event onsets in most of the analyzed wrist EMG segments
was reasonably clean, because wrist EMG has a fairly good SNR. Although the changes in the
baseline fluctuation are not ignored, which can be seen in the small peaks of the detection
statistics, overall they are significantly smaller than the change due to muscle activity increase
The sample movement-related event onset detection in a trunk muscle signal is shown in
Figure 6.
0 500 1000 1500 2000 2500 3000 3500 4000-0.1
-0.05
0
0.05
0.1
n (ms)
Original EMG signal
EMG
onset
0 500 1000 1500 2000 2500 3000 3500 40000
2
4
6x 10
-4
n (ms)
Dn statistic
Dn
onset
0 500 1000 1500 2000 2500 3000 3500 40000
10
20
30
n (ms)
Cumulative sum statistic
CUSUM
onset
Figure 6: Sample detection results for trunk muscles EMG (a) Original EMG signal, (b) Dn detection statistic,
(c) CUSUM detection statistic. Red circle marks the computed EMG onset.
38
The change-point analysis statistics computed from the trunk muscles EMG produce many
more peaks than the corresponding statistics from wrist muscles. This is due to much noisier
nature of the recordings from the trunk muscles, which have lower SNR. As a result, the
misdetections of EMG events by change-point analysis, as well as cases when change-point
analysis cannot detect relevant change at all become more common.
5.2. Frequency of Successful EMG Movement-related Events Detection by
Different Methods in Wrist Muscles
Frequency of successful EMG event detection is assessed for every recorded file by counting
the number of detected onsets in the vicinity of the expected muscle activation time out of the
total number of segments in which detection was attempted. For the wrist EMG signals the
expected event location was between 3000 and 4000ms. In some cases there was some EMG
activity greater than the baseline level but smaller than the main muscle activation event, some
events were detected between 2800 and 3000 ms such detections were also counted as
successful. The calculated successful detection frequencies for wrist muscles are presented in
Table 1. Frequency of successful detection does not provide an indication of correctness or
precision of the estimates, but rather shows how often the detection is unsuccessful.
Table 1: Frequency of Successful Movement-related Event Detection in Wrist EMG for Different Computer
Methods. Filenames show the coded participant ID (i.e. AAA1) whether recording was off medication
(OFFMED) or on medication (ONMED), and whether the recorded task was internally (INT) or externally
(EXT) triggered.
File Name Change-point
Analysis
Hodges & Bui Denoising +
Hodges & Bui
AAA1 OFFMED1 EXT 100% (43/43) 100% (43/43) 100% (43/43)
AAA1 OFFMED2 EXT 100% (44/44) 95% (42/44) 91% (40/44)
AAA1 OFFMED INT 94% (44/47) 91% (43/47) 72% (34/47)
AAA1 ONMED1 EXT 94% (33/35) 94% (33/35) 91% (32/35)
AAA1 ONMED2 EXT 100% (38/38) 100% (38/38) 97% (37/38)
AAA2 OFFMED1 EXT 100% (35/35) 91% (32/35) 100% (35/35)
AAA2 OFFMED2 EXT 100% (37/37) 97% (36/37) 100% (37/37)
AAA2 OFFMED3 EXT 95% (21/22) 100% (22/22) 100% (22/22)
AAA2 OFFMED1 INT 100% (28/28) 96% (27/28) 96% (27/28)
AAA2 OFFMED2 INT 100% (39/39) 90% (35/39) 92% (36/39)
AAA3 OFFMED1 EXT 100% (43/43) 100% (43/43) 100% (43/43)
AAA3 OFFMED2 EXT 100% (44/44) 98% (43/44) 100% (44/44)
AAA3 ONMED1 EXT 100% (44/44) 100% (44/44) 100% (44/44)
AAA3 ONMED INT 99% (76/77) 99% (76/77) 65% (50/77)
39
AAA4 OFFMED1 EXT 39% (17/44) 100% (44/44) 73% (32//44)
AAA4 OFFMED2 EXT 100% (44/44) 100% (44/44) 89% (39/44)
AAA4 OFFMED3 EXT 14% (6/44) 100% (44/44) 86% (38/44)
AAA4 OFFMED4 EXT 48% (21/44) 100% (44/44) 80% (35/44)
AAA4 OFFMED1 INT 31% (20/65) 98%(64/65) 0% (0/65)
AAA4 OFFMED2 INT 92% (101/110) 81% (89/110) 1% (1/110)
AAA5 ONMED1 EXT 100% (42/42) 100% (42/42) 100% (42/42)
AAA5 ONMED2 EXT 98% (41/42) 100% (42/42) 100% (42/42)
AAA5 ONMED INT 79% (61/77) 62% (48/77) 49%(38/77)
AAA6 OFFMED1 EXT 100% (40/40) 100% (40/40) 100% (40/40)
AAA6 OFFMED2 EXT 100% (35/35) 100% (35/35) 100% (35/35)
AAA6 OFFMED1 INT 100% (43/43) 100% (43/43) 79% (34/43)
AAA6 OFFMED2 INT 100% (47/47) 98% (46/47) 81% (38/47)
AAA6 ONMED1 EXT 100% (41/41) 100% (41/41) 100% (41/41)
AAA6 ONMED2 EXT 100% (42/42) 100% (42/42) 100% (42/42)
AAA6 ONMED1 INT 100% (92/92) 87% (80/92) 60% (55/92)
AAA7 OFFMED1 EXT 100% (38/38) 100% (38/38) 100% (38/38)
AAA7 OFFMED2 EXT 100% (24/24) 100% (24/24) 100% (24/24)
AAA7 OFFMED INT 99% (85/86) 88% (76/86) 77% (66/86)
AAA7 ONMED EXT 100% (37/37) 100% (37/37) 100% (37/37)
AAA7 ONMED INT 100% (69/69) 97% (67/69) 75% (52/69)
AAA8 OFFMED1 EXT 100% (33/33) 94% (31/33) 100% (33/33)
AAA8 OFFMED1 INT 100% (57/57) 100% (57/57) 95% (54/57)
AAA8 OFFMED2 INT 100% (31/31) 97% (30/31) 94% (29/31)
AAA8 ONMED1 EXT 100% (44/44) 98% (43/44) 98% (43/44)
AAA8 ONMED2 EXT 100% (44/44) 100% (44/44) 100% (44/44)
AAA8 ONMED1 INT 100% (36/36) 100% (36/36) 86% (31/36)
AAA8 ONMED2 INT 100% (37/37) 100% (37/37) 97% (36/37)
AAA9 OFFMED1 EXT 95% (37/39) 100% (39/39) 100% (39/39)
AAA9 OFFMED2 EXT 100% (20/20) 100% (20/20) 100% (20/20)
AAA9 OFFMED INT 95% (19/20) 95% (19/20) 50% (10/20)
AAA9 ONMED1 EXT 97% (34/35) 91% (32/35) 89% (31/35)
AAA9 ONMED2 EXT 96% (22/23) 96% (22/23) 96% (22/23)
AAA9 ONMED INT 100% (40/40) 90% (36/40) 33% (13/40)
Overall, the frequency of detection for the change-point method was comparable and often
higher than the detection frequency of the threshold-based methods. In most cases the frequency
of onset detection exceeded 90%. It is, however, notable that most of the recordings of the
participant AAA4 the onset detection frequency was rather low 14-48%. This is because
participant AAA4 had tremor, thus, the regular wrist muscles EMG was contaminated by tremor-
related spikes. Figure 7 shows the sample event detection in the EMG with tremor.
40
Figure 7: Detection of movement-related event in EMG signal contaminated by tremor. Top plot shows the
original raw signal with tremor spikes to which change-point analysis is applied. Second plot shows the
filtered and rectified signal from which the Hodges-Bui estimate is computed, and which does not have
tremor spikes which were removed by filtering, thus providing the best estimate. Third plot shows the
wavelet-denoised signal from which wavelet-based estimate was obtained. Lowest plot shows the CUSUM
statistic with the changes detected both due to tremor spikes and due to movement-related muscle activation,
with the changes due to tremor influencing the change-point statistic stronger.
The top plot in Figure 7 shows the raw signal, where the muscle activation is between 3000
and 4000 ms, and other peaks are due to tremor. When the signal is filtered from 30 to 200 Hz
(second plot), these peaks are removed, thus in this case the direct application of Hodges & Bui
algorithm yields the best results. Denoising (third plot) does not eliminate the tremor-related
peaks, but Hodges & Bui algorithm applied to a denoised signal still makes an estimate in the
expected time range (at least between 3000 and 4000 ms). The change-point algorithm detects all
the changes promptly, both those due to tremor and due to movement onset, however, the
criterion that the change due to movement is the largest of these changes frequently fails. To
maximize the detection of EMG onsets in the signal with tremor, filtering may thus be
unavoidable.
41
5.3. Frequency of Successful EMG Movement-related Events Detection by
Different Methods in Trunk Muscles
Computing the frequency of successful detection for the trunk muscles EMG is more
challenging since not all the trunk muscles contracted during the perturbed sitting. Therefore, the
frequency of onset detection was found only among the signals for which the presence of the
muscle activation event was confirmed with the assistance of visual detection experts. Because
of a large number of trunk muscle recordings (520 data files), the onset detection frequency was
only evaluated for the representative 16 data files collected from two experimental subjects for
which EMG muscle activation events onsets were visually estimated.
Table 2: Frequency of Successful Movement-related Event Detection in Trunk EMG for Different Computer
Methods. Filenames show the participant ID and directions of perturbation (middle digit of the numerical
code) according to Figure 2 from the Subsection 4.1.2.
File Name Change-point
Analysis
Hodges & Bui Denoising + Hodges & Bui
Subject 1 211 10/11 9/11 10/11
Subject 1 221 10/10 7/10 7/10
Subject 1 231 11/12 12/12 12/12
Subject 1 241 10/14 12/14 13/14
Subject 1 251 11/13 12/13 11/13
Subject 1 261 11/12 12/12 12/12
Subject 1 271 4/6 4/6 5/6
Subject 1 281 7/12 9/12 10/12
Subject 2 211 6/7 7/7 7/7
Subject 2 221 6/11 11/11 11/11
Subject 2 231 8/15 14/15 15/15
Subject 2 241 6/11 10/11 11/11
Subject 2 251 7/11 11/11 11/11
Subject 2 261 7/12 11/12 9/12
Subject 2 271 3/8 8/8 8/8
Subject 2 281 4/8 7/8 8/8
It is notable that although the onset detection for change-point analysis has been reasonably
consistent for Subject 1 recordings, the frequencies of detection for Subject 2 were rather low.
The nature of the problem was similar to the tremor case described in Section 5.2 there were
multiple changes in the signal segments, sometimes due to multiple muscle activations,
sometimes due to some additional events, such as EKG and crosstalk-related artefacts, and
artefacts due to poor electrode contact with the skin. Thus, the change-point detection statistic
42
increase corresponding to the EMG movement-related event was in many cases smaller than
such an increase due to other activity. For example, in a noisy signal, extreme spikes due to
outlier values generate peaks in detection statistics, which can be bigger than the other changes
in the signal structure (Moskvina et. al., 2003). An example when a misdetection of event onset
occurred is shown in Figure 8.
Figure 8: An example of EMG event misdetection by the change-point analysis algorithm in trunk EMG. Top
plot shows the original signal from one of the trunk muscles. Second plot shows the filtered and rectified
signal from which the Hodges-Bui estimate is computed. Third plot shows the wavelet-denoised signal from
which wavelet-based estimate was obtained. Lowest plot shows the CUSUM statistic with multiple changes
detected in sequence with some of the later changes having bigger influence on the detection statistic than the
earlier ones, although earlier smaller changes are unanimously identified by visual estimators as the onset of
movement-related event.
In this case one can observe the increased activity of the muscle around 1500 ms from the
start of the data segment; this is evident in all the shown plots – on the raw, filtered and denoised
signals. In fact, the CUSUM statistic also shows its first large peak around this time as well. This
is a location selected by visual estimators as the EMG movement-related event onset. However,
one can also observe a larger activity around 2000ms from the start of the segment (again
reasonably visible on raw, filtered and denoised signals). This activity corresponds to the largest
43
peak on the CUSUM statistic plot and it is thus selected as the EMG event onset by the change-
point detection algorithm, which disagrees with the visual estimates.
5.4. Quality of Movement-related Events Detection by Different Methods in
Wrist Muscles
For the datasets for which visual estimates of EMG movement-related events onsets were
collected it was possible to assess the quality of the computer methods’ onset calculations. This
was done to ensure that the change-point detection method is at least as accurate as the other
tested computer methods for the purpose of EMG event detection. The visual estimates of onsets
of EMG events in wrist muscles were made by 3 evaluators, trained in EMG signal processing,
for 9 datasets recorded from different individuals. In these datasets, the segments for which at
least one of the computer methods was not successful were removed from the quality calculation.
This allowed making sure that the quality of the computer methods is assessed over the same
segments.
To evaluate the quality of the estimates two methods were used. The first one is to compute
the average absolute differences between three visual estimates and each of the computer
estimates in all used segments. After that the average absolute differences within the same
dataset can be compared using statistical tests to verify if they are significantly bigger or smaller
depending on the chosen computer method. Normality of the distributions of the sets of average
absolute differences for computer methods was tested using Lilliefors test (MATLAB command
lillietest) for normality, and in many cases the tests showed that distributions of these differences
were not normal, thus regular parametric methods could not be applied. Therefore, to perform
the analysis of distributions of average absolute differences, the Kruskal-Wallis nonparametric
test was applied (MATLAB command kruskalwallis); it is the analog of the 1-way ANOVA for
cases when it is not known for sure that the random variables that are being tested have normal
distributions required for regular ANOVA (Wackerly et. al., 2002). Kruskal-Wallis test was
followed by multiple comparisons test (MATLAB command multcompare) which provided
information on whether the sets of average absolute differences for computer methods were
significantly different from each other pairwise. The summary of computer detection quality
measurement as average absolute differences between visual and computer estimates is shown in
Table 3. The plots of average absolute differences for different segments, Kruskal-Wallis /
ANOVA tables and plots of multiple comparison tests plots are presented in Appendix E.
44
Table 3: Quality of Movement-related Events Onset Detection Assessed by Mean Ranks of Average Absolute
Differences between Visual Estimates and Computer Methods in Wrist EMG Signals (mean rank ± standard
error). Filenames show the coded participant ID (i.e. AAA1). All the recordings whose results are presented
in this table were externally triggered (EXT) and were recorded off medication (OFFMED) or on medication
(ON)
Mean Ranks ± Standard Error File Name
Change-point
Analysis
Hodges & Bui Denoising + Hodges
& Bui
AAA1 OFFMED1 EXT 50.4302 ± 5.7007 69.8372 ± 5.7007 74.7326 ± 5.7007
AAA2 OFFMED1 EXT 44.3750 ± 4.9242 67.5313 ± 4.9242 33.5938 ± 4.9242
AAA3 OFFMED1 EXT 69.1163 ± 5.7005 46.5814 ± 5.7005 79.3023 ± 5.7005
AAA4 OFFMED1 EXT 16.0000 ± 2.9150 11.5455 ± 2.9150 23.4545 ± 2.9150
AAA5 ONMED1 EXT 69.9881 ± 5.6345 56.7619 ± 5.6345 63.7500 ± 5.6345
AAA6 OFFMED1 EXT 59.9250 ± 5.4994 49.5000 ± 5.4994 72.0750 ± 5.4994
AAA7 OFFMED1 EXT 55.6447 ± 5.3615 48.0395 ± 5.3615 68.8158 ± 5.3615
AAA8 OFFMED1 EXT 34.9250 ± 3.9047 31.3750 ± 3.9047 25.2000 ± 3.9047
AAA9 OFFMED1 EXT 37.4189 ± 5.2913 68.0270 ± 5.2913 62.5541 ± 5.2913
The mean ranks in Table 3 show if the average absolute differences in visual and computer
estimates are significantly different for different computer methods. Smaller mean ranks
correspond to smaller detection error relative to visual estimates. It is notable that in three
datafiles analyzed in this way (AAA1 and AAA9) the change-point detection method was
superior to other methods, for six files it was not statistically different from other methods, and
for one file (AAA3), it was statistically inferior to one computer method and comparable to the
other one.
The second way to compute the detection quality is to compute how much the estimates by
the visual detection correlate with the results produced by the computer tests. This is achieved by
evaluating the Spearman rank coefficient (MATLAB corr command), which is a nonparametric
method to test for correlation between two ranked variables (Wackerly et. al., 2002). To apply
the method, the mean value of three visual estimates for each processed segment was computed.
Then the Spearman rank coefficient was evaluated between these means and the sets of estimates
for each of the computer algorithms. The bigger Spearman coefficient shows that two time series
between which it is evaluated are more closely correlated. The Spearman rank statistical test
computation was also performed verifying that the computed correlation was not equal to zero.
The smaller the p-value associated with this test, the more likely it is that the correlation between
the two tested sets is non-zero. The results of Spearman coefficients calculations are presented in
Table 4.
45
Table 4: Quality of Movement-related Events Onset Detection Assessed by Spearman Rank Coefficients
between Visual Estimates and Computer Methods in Wrist EMG Signals. Filenames show the coded
participant ID (i.e. AAA1). All the recordings whose results are presented in this table were externally
triggered (EXT) and were recorded off medication (OFFMED) or on medication (ON)
Change-point
Analysis
Hodges & Bui Denoising + Hodges
& Bui
File Name
Spearman
Coeff.
p-value Spearman
Coeff.
p-value Spearman
Coeff.
p-value
AAA1 OFFMED1 EXT 0.7198 5.34e-08 0.6250 7.46e-06 0.2212 0.154
AAA2 OFFMED1 EXT 0.9592 5.21e-18 0.9465 2.82e-16 0.9709 3.47e-20
AAA3 OFFMED1 EXT 0.7005 1.70e-07 0.9092 3.39e-17 0.5700 6.61e-05
AAA4 OFFMED1 EXT 0.7062 0.0152 0.8242 0.00181 -0.1149 0.7365
AAA5 ONMED1 EXT 0.7586 5.88e-09 0.7512 9.93e-09 0.6733 1.03e-06
AAA6 OFFMED1 EXT 0.8957 6.06e-15 0.8875 2.34e-14 0.6204 1.95e-05
AAA7 OFFMED1 EXT 0.9505 7.42e-20 0.9800 7.93e-27 0.8995 1.65e-14
AAA8 OFFMED1 EXT 0.7424 1.78e-4 0.8605 1.13e-06 0.8060 1.98e-05
AAA9 OFFMED1 EXT 0.7698 2.55e-8 -0.2262 0.1782 0.3067 0.0648
Overall, according to Table 4, Spearman rank coefficient is showing similar assessment of
detection quality to average absolute differences comparison. For AAA1 and AAA9, the
correlations for the change-points analysis are the highest of the computer methods. For AAA2,
AAA3, AAA4 and AAA7, change-point analysis method has the second highest correlation
coefficient and for AAA8 – the lowest. These quality evaluations are consistent with the mean
ranks in Table 3, although the mean rank differences among the computer methods for most files
were not significant. For AAA6 and AAA5, the Spearman coefficient results and mean rank
results disagree, but perfect match was not expected since correlation and relative size of
discrepancies between visual and computer onsets are two fairly different quantities. However,
because there are no error bounds on the Spearman coefficients, the mean ranks comparison is a
more reliable method to assess the detection quality.
5.5. Quality of Movement-related Events Onset Detection by Different Methods
in Trunk Muscles
Quality of movement-related events onset detection in trunk EMG signals was assessed by
the same methods as those used in wrist EMG: computation of average absolute differences
between visual and computer estimates and correlation between visual and computer estimates.
The visual estimates of onsets of trunk muscle movement-related events were made by 3
46
evaluators, experts in EMG signal processing, in 16 datasets recorded from two individuals. In
these datasets, the segments for which at least one of the computer methods was not successful
were removed from the quality calculation. Each particular data file had only 16 EMG segments,
and not all of these contained an activation of muscle. Besides that, not all computer methods
succeeded for all segments. Therefore, all EMG segments from 8 data files for each experiment
subject for which there were three visual and three computer onset estimates were combined for
the statistical analysis. Thus, there were a total of 64 EMG segments for Subject 1 and 42
segments for the Subject 2 that were used for the quality calculations. The results for mean ranks
comparison and Spearman coefficients are presented in Tables 5 and 6. The plots of average
absolute differences for different segments, Kruskal-Wallis / ANOVA tables and plots of
multiple comparison tests plots are presented in Appendix F.
Table 5: Quality of Movement-related Event Onset Detection Assessed by Mean Ranks of Average Absolute
Differences between Visual Estimates and Computer Methods in Trunk EMG Signals (mean rank ± standard
error)
Mean Ranks ± Standard Error Name
Change-point
Analysis
Hodges & Bui Denoising + Hodges &
Bui
Subject 1 95.9609 ± 6.9461 98.2188 ± 6.9461 95.3203 ± 6.9461
Subject 2 87.5000 ± 5.7008 53.5814 ± 5.7008 53.9186 ± 5.7008
Table 6: Quality of Movement-related Event Onset Detection Assessed by Spearman Rank Coefficients
between Visual Estimates and Computer Methods in Trunk EMG Signals
Change-point
Analysis
Hodges & Bui Denoising + Hodges &
Bui
Name
Spearman
Coeff.
p-value Spearman
Coeff.
p-value Spearman
Coeff.
p-value
Subject 1 0.7841 1.83e-14 0.8674 1.86e-20 0.9011 3.49e-24
Subject 2 0.6238 7.87e-06 0.6377 4.24e-06 0.7009 1.66e-07
The mean ranks for the change-point method for Subject 2 are significantly larger than those
for other computer methods, which means that it was less accurate than other methods. For
Subject 1, the differences in accuracies of computer methods are not statistically significant, thus
the change-point method is not inferior to other ones. Results of Spearman rank coefficients are
less conclusive since estimated coefficients are rather close to each other for all computer
methods.
5.6. Summary of the Chapter
47
In Chapter 5 the results of EMG movement-related event detection techniques and their
comparison were presented. The sample detection statistic plots were shown in Section 5.2.
Sections 5.3 and 5.4 contained the results on the frequency of successful detection for different
computer algorithms for wrist and trunk muscles respectively. Overall, for wrist muscles EMG
the change-point method shows comparable, if not superior, success of event onsets detection,
except for the data files containing EMG with tremor, in which the changes in the signal due to
tremor contributed to larger increases of the detection statistics than the changes due to muscle
activation. However, it is inferior for trunk muscles due to noisier signal and larger number of
changes per signal segment, when some of the changes unrelated to movement onset have large
impact on the detection statistic. Sections 5.5 and 5.6 presented two ways to assess the detection
quality: by comparing the average absolute differences for computer methods using Kruskal-
Wallis test and multiple comparisons test and by computing the correlation between visual and
computer detection results using Spearman rank coefficients. Change-point analysis method
shows comparable quality of onset detection to other computer methods for wrist data, and for
the data from one of the trunk recordings subject, however, for the other trunk experiment
subject, whose data is analyzed, the quality of change-point based detection was inferior. The
results of frequency and quality of detection are summarized in Tables 1-6.
48
Chapter 6: Discussion
In this chapter, relevant issues related to the change-point detection application to EMG
movement-related events onset detection, and its results will be discussed.
6.1. Benefits of Change-point Detection in the EMG Processing Application
Change-point analysis allows the detection of multiple changes in signals’ statistical
properties. The advantage of the technique is that it is applicable to raw signals, which do not
need to be rectified and filtered. SSA-based change-point detection procedure automatically
denoises the signal, which is very important for EMG signals whose recording is frequently
noisy. This effect is achieved because when the signal is decomposed by SSA into components,
those that represent noise can be eliminated from the computation of detection statistics.
Similarly, the SSA procedure can allow removing periodic components from the change-point
calculations or on the contrary to extract them and detect changes in these components.
Fluctuation of the baseline level does not strongly affect the detection. Another advantage of the
technique is that it can work with fairly short signal segments. This is valuable because
frequently the pieces of signal that correspond to a movement phenomena are short, and might
not contain enough points for more advanced computational techniques. It was shown in this
thesis that for wrist EMG muscles, the events onsets determined as the biggest changes shown by
change-point analysis shows detection frequency and accuracy comparable to the threshold-
based methods without or with denoising, which is shown in the results of Sections 5.3 and 5.5.
For the trunk muscle more visual estimates are needed to be able to judge on the accuracy and
detection frequency of change-point method better, but for one of the two individuals for which
the visual estimates were obtained, accuracy and detection frequency were comparable with
other methods.
Change-point analysis can also be used for retrospective analysis of the data and for real-time
applications. When analysing EMG signals from multiple muscles recorded simultaneously
which may or may not have clear muscle activations, one can study the relative times of changes,
as well as the synchronicity of the changes, i.e. if certain muscles are activated or deactivated at
the same time.
49
6.2. Limitations of the Change-point Detection in the EMG Processing
Application
First important drawback of change-point detection when applied to EMG processing is the
inability to recognize the movement-related event onset among the multiple changes present in
the signal which may or may not be related to muscle activation. Although many changes are
being detected in the same processing run, it is the easiest to determine the onset when one
change is significantly bigger than the others – in this case this dominant change corresponds to
the increase of muscle activity. This was the case in most of the wrist muscle EMG segments.
However, in the wrist EMG with tremor and in trunk EMG there were many changes causing
similar increases of the detection statistics. The largest change did not correspond to the
movement-related event in many cases, so the hypothesis proposed in Section 3.2 did not hold.
For example, in the EMG with tremor, the peaks of the detection statistic due to tremor were
comparable in height and frequently higher than those due to increased muscle activity, as shown
in Figure 7, Section 5.3. In the case of tremor, one could filter the signal for the purpose of
removing the tremor peaks, but the purpose of the change-point analysis application was to test
its ability to process the raw signals. In the trunk muscles EMG signals there were either multiple
small activations of muscle in a sequence, or multiple activations at different times of the
recording, so in many cases the first observed significant change which corresponded to the
EMG event onset detected by the visual estimators was in many cases not the largest of the
changes which was selected as the event onset by the change-point analysis algorithm. The
example of this is shown in Figure 8, Section 5.4. Unfortunately, the change-point detection does
not give the tools to classify the changes by origin; it only finds locations in time where the
changes happened. Therefore, in order to make sure that onset locations were meaningful it is
necessary to manually check the data segments to ensure that the computed onsets fall in the
vicinity of the expected positions.
One has to acknowledge that the method applied in this study to determine the accuracy of
the detection was not the most optimal. Since real recorded EMG signals were used, true EMG
event onsets were not known before the application of detection methods. There was no
kinematic data to be able to define precisely when movement occurred. Visual estimates were
subjective; the results of such EMG event detection depended on the estimators’ experience, and
the amount of time they spent per signal segment. In addition to that, different EMG segments
recorded from the same person under the same conditions may contain individual features that
50
could be interpreted differently by observers, which may have affected the onset detection, for
example, a small activity increase (compared to the baseline) preceding the increase,
corresponding to actual movement onset. The more objective way to study the accuracy of
different computer techniques is to use modeled EMG signals in which the location of
movement-related event onset is precisely controlled. For example, a useful modeling approach
was proposed by Staude et. al. using the autoregressive model through which white noise with a
time-varying variance is passed through, and the variance changes from the inactive level to
active one at the time controlled by the experimenter (Staude et. al., 2001). While the modeling
overall would allow estimating the accuracy better, the particular approach proposed by Staude
et. al. may give some advantage to the change-point method, because SSA should be able to
calculate a precise fit to the EMG modeled as an autoregressive signal with finite number of
terms (Moskvina et. al., 2003). An alternative would be to repeat the EMG recordings with some
concurrent kinematic measurement, for example, to use the goniometer to record the joint angle
during wrist extension movements or the accelerometer to record the trunk behaviour due to
perturbations in different directions. Then there would be some fixed time difference between the
onset of kinematic movement measurement and the onset of EMG movement related-event for
the same muscle in the same subject, as suggested, for example, by (David, 2003), which would
help making the assessment of quality of EMG event detection more objective, and eliminate the
need of visual detection for comparison of algorithms. This would also allow comparing the
accuracy of computer method to that of visual detection method.
There is another problem with assessment of quality in the way presented in Chapter 5. Two
methods were presented, both using nonparametric statistical tests. Mean ranks of differences
essentially tell how close (distance) the computer estimates are to visual ones; lower mean ranks
meaning higher “quality”. Spearman rank coefficients provide the measure of correlation
between visual and computer onsets; higher coefficient showing higher “quality”. However,
these two measures do not assess the same thing. It is, for example, possible to have the values
computed by the algorithm to be close to visual estimates (i.e., have lower mean ranks), but not
to correlate well with the visual estimates (have low Spearman coefficient and high p-value in
the test for non-zero correlation). The discrepancy of this sort was indeed observed for AAA5
and AAA6 in Tables 3 and 4 in Section 5.5, where the mean rank was showing higher quality,
while Spearman coefficient showed lower one. Mean ranks have error bounds accompanying
them, so they may be a more reliable way to assess quality of detection than the rank
coefficients.
51
6.3. Issues Worthy of Further Investigation
In the described change-point detection experiment, the effects of parameters of the algorithm
on the frequency and accuracy of change-point detection were not investigated. No precise
tuning was attempted in this experiment. Instead, the objective was to try out utility of change-
point analysis to EMG movement-related events detection. All parameters were selected rather
crudely. Selection of the lag parameter equal to 50 meant that an attempt of constructing the
model of the signal with 50 components, which was believed to be a sufficient (and perhaps
superfluous) approximation of the order of the EMG signal, and was not interfering with the
main frequencies 30-200 Hz of the EMG. Other parameters were selected essentially depending
on the choice of the lag parameter (described in Subsection 4.3.1). However, other approaches to
parameter choice were possible. One possibility is a more precise determination of suitable lag
parameter. This is particularly important because the method involves fairly bulky computations
with matrices and when these matrices are big, the algorithm works slowly. This is relevant, for
example, when change-point analysis is used for change detection in real time, so speeding up
the calculations is desirable, while maintaining a reasonable accuracy. Another issue is to
investigate the number of components used for the calculation of the detection statistics. In the
present implementation, the number of these components changed for every data segment to
include all components whose eigenvalues exceed 5% of the total sum of eigenvalues. Instead it
may be useful to investigate keeping this number of components fixed at some reasonable value,
say 5-10, to ensure that at least a certain number of components were used to compute detection
statistics for all segments. Other parameters tuning can also be investigated. For example, by
increasing a window length m to values larger than twice the lag parameter some small changes
could be smoothed out, highlighting the larger ones.
It is also useful to look for better ways to identify the onset from the change-point detection
statistics. These can include some thresholds for the increase of the statistics from the baseline
level, or perhaps finding a region of the statistic where several significant changes occur in
succession. Another possibility is to check for how long the CUSUM statistic stays above zero or
above some threshold for different peaks. In the wrist EMG the duration of the common muscle
activation due to movement is about 500 – 600ms (see Figure 5 in Section 5.1 and Figure 7 in
Section 5.2) while spikes due to tremor last for about 100-200ms (see Figure 7, Section 5.2.),
52
such a time parameter may provide a better way to tell from the detection statistic which change
actually corresponds to the movement onset, than just using the point, from which the highest
peak originated.
Another interesting investigation is an application of a different change-point detection
technique also based on subspace identification for comparison with SSA-based algorithm and
other methods. This is the SSM method (Kawahara et. al., 2007), mentioned in Subsection 2.2.2.
It may be able to identify the signal structure better than SSA because it is more general than
SSA method, and may be more consistent in identifying the movement-related EMG event as the
main change present in the signal. Besides that, it may be worthwhile to consider some
combination of methods, for example, application of threshold-based detection to the CUSUM or
even Dn statistic.
6.4. Summary of the Chapter
In this chapter, relevant issues and concerns raised by the observed onset detection results
using change-point detection were discussed. In Section 6.1 the possible benefits of the change-
point analysis were discussed, including processing raw EMG signals without filtering,
denoising and rectification, and applications, for example, studying the synchronicity of muscle
activations. In Section 6.2, limitations of change-point detection and of the described EMG
application experiment are mentioned. In this section, the problem that the largest change does
not always correspond to movement onset was discussed. Other limitations included the use of
raw data with visual onset estimates to study accuracy of computer methods, lack of kinematic
data to be able to objectively define the movement onsets and potential disagreement of two
ways to assess the quality of the detection. In Section 6.3 some issues related to improving the
algorithm performance were listed. In particular, these include investigating the fine-tuning of
the algorithm parameters to improve speed and accuracy, and studying different decision rules
based on the detection statistics that could tell which detected change actually corresponds to
EMG onset. The possibility of using alternative detection methods is also mentioned.
53
Chapter 7: Conclusion and Future Work
The application of subspace identification based method of change-point analysis to EMG
signals was presented. The algorithm for analysis was described in Moskvina et. al., 2003. It
involved performing a singular spectrum decomposition of the trajectory matrix formed from the
signal preceding a hypothetical change-point into principal components. Then the distance is
computed between the most important components of this trajectory matrix and the columns of
the test matrix, formed from the signal after the hypothetical change-point. If there was a big
increase in the values of this distance, it meant that a change occurred.
The change-point algorithm was applied to detect the onsets of the EMG movement-related
events in signals recorded from the wrist and trunk muscles along with two other computer-based
methods: regular Hodges&Bui algorithm (Hodges et. al., 1996) and Hodges&Bui algorithm
preceded by Donoho’s denoising (Donoho, 1995). Also visual estimates were obtained from
three people trained in EMG signal processing. In terms of change-point analysis, the onsets
were defined as the point at which the increase of the detection statistic started that led to
reaching its maximum value. The frequencies of successful onset detection were computed for
three computer algorithms. Also the quality of detection was measured by computing average
absolute differences between computer and visual estimates and comparing these differences
using Kruskal-Wallis nonparametric test. In addition to that, the Spearman rank coefficients were
computed between the visual and computed onsets to see which computer method produces the
estimates
It was found that for most of the wrist EMG data the change-point analysis method is
comparable and often superior to the other computer methods investigated both in terms of
detection frequency and quality. However, for the trunk muscles EMG and for wrist EMG with
tremor, the change-point analysis did not perform as well as the threshold-based methods,
primarily because the largest detected change in these signals did not necessarily correspond to
the movement onset
Change-point analysis based on SSA may find other applications in the processing of
biological signals. Besides analysis of EMG signals, the detection of changes in heart rate
(described in Warrick et. al., 2007) or in the EEG and deep brain recording may constitute
valuable uses for this technique. Investigation of the parametric settings to improve algorithms
speed and accuracy as well as the development of some decision-making techniques using the
54
computed detection statistics (like establishing better thresholds for changes) should make the
SSA-based change-point detection technique well suitable for retrospective and real-time
biological signal processing applications.
55
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Appendices
Appendix A: Change-point Detection Algorithm MATLAB Implementation
function [cp_list1, cp_list2, D, W]=ssa_cp_find_high_threshold(x1,m,M,p,q)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% -----------------------------------------------------------------
% SSA implementation
% Author: Francisco Javier Alonso Sanchez e-mail:[email protected]
% Departament of Electronics and Electromecanical Engineering
% Industrial Engineering School
% University of Extremadura
% Badajoz
% Spain
% -----------------------------------------------------------------
% Change-point detection Implementation by Lev Vaisman
% Institute of Biomaterials and Biomedical Engineering
% University of Toronto, Toronto. Ontario, Canada
% -----------------------------------------------------------------
% x1 Original time series (column vector form)
% m - window width of the data on which to operate at a time, must be even
% M - Lag length
% p and q – test matrix parameters
% introductory definitions
N=length(x1);
if M>m/2;M=m-M;end
if nargin==3
p=m-M+1;
q=m+1;
end
% step 3 and 4: sum of eigenvalues and choosing L
K=m-M+1;
X_big=zeros(M,K);
for (i=1:K) X_big(1:M,i)=x1(0+(i:i+M-1)); end
S=X_big*X_big';
[U,autoval]=eig(S);
[d,i]=sort(-diag(autoval));
d=-d;
sev=sum(d);
d./sev*100;
lgth=length(find((d./sev)*100>5));
L=1:lgth
% running the procedure for all n from 0 to N-m-M
for n=0:N-m-M
% step1 : building trajectory matrix
K=m-M+1;
X=zeros(M,K);
62
for (i=1:K) X(1:M,i)=x1(n+(i:i+M-1)); end
% step 2 : SVD
S=X*X';
[U,autoval]=eig(S);
[d,i]=sort(-diag(autoval));
U=U(:,i);
UL=U(:,L);
% computing distances of trajectory matrix to L eigenvectors
DX=0;
for i=1:K
DX=DX+((X(:,i)')*X(:,i)-(X(:,i)')*UL*(UL')*X(:,i));
end
v(n+1)=DX./(M*K);
% step 5 : form test matrix
T=zeros(M,q-p);
for (i=p+1:q)
T(1:M,i-p)=x1(n+(i:i+M-1));
end
% step 6: computing distances of test matrix to L eigenvectors
DnLpq=0;
for i=1:(q-p)
DnLpq=DnLpq+((T(:,i)')*T(:,i)-(T(:,i)')*UL*(UL')*T(:,i));
end
D(n+1)=DnLpq./(M*(q-p));
if n>m/2
SN(n+1)=D(n+1)/v(m/2+1);
else
SN(n+1)=D(n+1)/v(n+1);
end
% step 7: computing a CUSUM statistic
if n==0
W(n+1)=SN(n+1);
else
W(n+1)=max(W(n)+SN(n+1)-SN(n)-1./(sqrt(M*(q-p))),0);
end
end
% detecting change-points
% from Dn Statistic
k=0;
for i=2:length(D)-1
if D(i)<D(i+1)&&D(i)<D(i-1)
k=k+1;
cp_list2(k)=i+M+m;
end
end
% from CUSUM statistic
threshold=8/sqrt(M*(q-p-2))
k=0;
63
for i=1:length(W)
if W(i)>threshold
for j=1:i-1
if W(i-j)==0
k=k+1;
if k==1||cp_list1(k-1)~=i-j+1+m+M
cp_list1(k)=i-j+1+m+M;
else
k=k-1;
end
break;
end
end
end
end
64
Appendix B: Script to Input the Visual Estimates of the EMG Onsets with a Mouse
in MATLAB
clear load aaa1_offmed1_ext_rawandfiltered.mat % ginput command takes coordinates of mouse click
for i=1:size(RWE,2) plot(RWE(:,i),'b') title(i) [x_KM(i),y_KM(i)]=ginput(1) End
% rounding the click coordinate to the nearest millisecond x_KM=round(x_KM); save aaa1_offmed1_ext_visual_KM.mat x_KM y_KM % if you want raw EMG, replace RWE by emg_extract_offmed1_ext
65
Appendix C: Hodges&Bui algorithm Implementation in MATLAB
% computing the thresholds for Hodges and Bui % based on 500 ms before the trigger % filter EMG 30-200Hz load EMGfilter_30_200.mat
% for every EMG segment
for i=1:size(emg_extract_offmed1_ext,2) RWE(:,i)=abs(filtfilt(EMGfilter,1,emg_extract_offmed1_ext(:,i))); temp_mean(i,:)=[mean(RWE(2500:2599,i)) mean(RWE(2600:2699,i))
mean(RWE(2700:2799,i)) mean(RWE(2800:2899,i)) mean(RWE(2900:2999,i))]; [temp1 temp2]=find(temp_mean(i,:)==median(temp_mean(i,:)),1); emg_mean(i,:)=temp_mean(i,temp2); switch temp2 case 1 emg_std(i,:)=std(RWE(2500:2599,i)); case 2 emg_std(i,:)=std(RWE(2600:2699,i)); case 3 emg_std(i,:)=std(RWE(2700:2799,i)); case 4 emg_std(i,:)=std(RWE(2800:2899,i)); case 5 emg_std(i,:)=std(RWE(2900:2999,i)); end for n=1:2950 tmp=mean(RWE(3000+n:3000+n+50,i)); if tmp>emg_mean(i,:)+3*emg_std(i,:) onsetHB_offmed1_ext(i)=3000+n; break; end end end
66
Appendix D: Wavelet-based Denoising Implementation in MATLAB
% % now apply denoising and then Hodges method % first rectify then denoise (Sin, 2007)
emg_denoised=wavelet_denoising(abs(emg_extract_offmed1_ext),14); % for every EMG segment
% compute threshold based on 500 ms before stimulus
for i=1:size(emg_extract_offmed1_ext,2) temp_mean(i,:)=[mean(emg_denoised(2500:2599,i))
mean(emg_denoised(2600:2699,i)) mean(emg_denoised(2700:2799,i))
mean(emg_denoised(2800:2899,i)) mean(emg_denoised(2900:2999,i))]; [temp1 temp2]=find(temp_mean(i,:)==median(temp_mean(i,:)),1); emg_mean(i,:)=temp_mean(i,temp2); switch temp2 case 1 emg_std(i,:)=std(emg_denoised(2500:2599,i)); case 2 emg_std(i,:)=std(emg_denoised(2600:2699,i)); case 3 emg_std(i,:)=std(emg_denoised(2700:2799,i)); case 4 emg_std(i,:)=std(emg_denoised(2800:2899,i)); case 5 emg_std(i,:)=std(emg_denoised(2900:2999,i)); end for n=1:2950 tmp=mean(emg_denoised(3000+n:3000+n+50,i)); if tmp>emg_mean(i,:)+3*emg_std(i,:) onsetVD_offmed1_ext(i)=3000+n; break; end end end
% wavelet-based denoising code (provided by V. Sin)
% version for trunk muscles
% Wavelet denoising
% levels =14 was the used value of the parameter for levels of decomposition
function denoised=wavelet_denoising(noisy, levels)
% extra rectification (just in case non-rectified signal was sent in)
emg_ens=abs(noisy');
r=size(emg_ens,1);
% r is length of signal
filttype='haar';
for j=1:r
tempsignal=emg_ens(j,1:1000);
[C,L]=wavedec(tempsignal,levels,filttype);
%determining the coefficients and variance
tempsum=L(1);
for k=2:levels+1
a=tempsum+1;
b=L(k)+tempsum;
67
d1=C(a:b);
tempsum=b;
db=mean(d1);
s2=var(d1-db);
delta(k-1)=sqrt(s2);
s2struct(k-1)=s2;
end
%decomposing the signal of interest
tempsignal=emg_ens(j,:);
[C,L]=wavedec(tempsignal, levels, filttype);
xs=zeros(size(C));
tempsum=L(1);
for k=2:levels+1
a=tempsum+1;
b=L(k)+tempsum;
d1=C(a:b);
temp=max(abs(d1)-delta(k-1),zeros(1,length(a:b)));
xs(a:b)=sign(d1).*temp;
tempsum=b;
end
%reconstructing the modified signal
temprec=waverec(xs,L,filttype);
emg_ens(j,:)=temprec-mean(temprec(1,1:1999));
end
denoised=emg_ens';
68
Appendix E: Average Absolute Differences Plots, Kruskal-Wallis / ANOVA
Tables and Multiple Comparisons Plots for Wrist Muscle EMG
0 5 10 15 20 25 30 35 40 450
50
100
150
200
250
300
350
400
450
segment #
avera
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bsolu
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illis
econds
Average Absolute Differences between Visual and Computer Estimates, AAA1
Wavelet denoising + Thresholding
Thresholding
Change-point analysis
Figure 9: AAA1 Average Absolute Differences
Table 7: AAA1 Kruskal-Wallis ANOVA
40 45 50 55 60 65 70 75 80 85
diffCP
diffHB
diffVD
Multiple Comparisons Test Plot, AAA1
2 groups have mean ranks significantly different from diffCP
Figure 10: AAA1 Multiple Comparisons Test
69
0 5 10 15 20 25 30 350
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350
segment #
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Average Absolute Differences between Visual and Computer Estimates, AAA2
Wavelet denoising + Thresholding
Thresholding
Change-point analysis
Figure 11: AAA2 Average Absolute Differences
Table 8: AAA2 Kruskal-Wallis ANOVA
20 30 40 50 60 70 80
diffCP
diffHB
diffVD
Multiple Comparisons Test Plot, AAA2
The mean ranks of groups diffCP and diffHB are significantly different
Figure 12: AAA2 Multiple Comparisons Test
70
0 5 10 15 20 25 30 35 40 450
50
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150
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250
300
segment #
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Average Absolute Differences between Visual and Computer Estimates, AAA3
Wavelet denoising + Thresholding
Thresholding
Change-point analysis
Figure 13: AAA3 Average Absolute Differences
Table 9: AAA3 Kruskal-Wallis ANOVA
30 40 50 60 70 80 90
diffCP
diffHB
diffVD
Multiple Comparisons Test Plot, AAA3
The mean ranks of groups diffCP and diffHB are significantly different
Figure 14: AAA3 Multiple Comparisons Test
71
1 2 3 4 5 6 7 8 9 10 110
50
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350
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500
segment #
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Average Absolute Differences between Visual and Computer Estimates, AAA4
Wavelet denoising + Thresholding
Thresholding
Change-point analysis
Figure 15: AAA4 Average Absolute Differences
Table 10: AAA4 Kruskal-Wallis ANOVA
5 10 15 20 25 30
diffCP
diffHB
diffVD
Multiple Comparisons Test Plot, AAA4
No groups have mean ranks significantly different from diffCP
Figure 16: AAA4 Multiple Comparisons Test
72
0 5 10 15 20 25 30 35 40 450
50
100
150
200
250
300
350
400
450
500
segment #
ave
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ab
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nd
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Average Absolute Differences between Visual and Computer Estimates, AAA5
Wavelet denoising + Thresholding
Thresholding
Change-point analysis
Figure 17: AAA5 Average Absolute Differences
Table 11: AAA5 Kruskal-Wallis ANOVA
45 50 55 60 65 70 75 80
diffCP
diffHB
diffVD
Multiple Comparisons Test Plot, AAA5
No groups have mean ranks significantly different from diffCP
Figure 18: AAA5 Multiple Comparisons Test
73
0 5 10 15 20 25 30 35 400
50
100
150
200
250
300
350
400
segment #
ave
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Average Absolute Differences between Visual and Computer Estimates, AAA6
Wavelet denoising + Thresholding
Thresholding
Change-point analysis
Figure 19: AAA6 Average Absolute Differences
Table 12: AAA6 Kruskal-Wallis ANOVA
40 45 50 55 60 65 70 75 80 85
diffCP
diffHB
diffVD
Multiple Comparisons Test Plot, AAA6
No groups have mean ranks significantly different from diffCP
Figure 20: AAA6 Multiple Comparisons Test
74
0 5 10 15 20 25 30 35 400
20
40
60
80
100
120
140
160
180
segment #
ave
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Average Absolute Differences between Visual and Computer Estimates, AAA7
Wavelet denoising + Thresholding
Thresholding
Change-point analysis
Figure 21: AAA7 Average Absolute Differences
Table 13: AAA7 Kruskal-Wallis ANOVA
35 40 45 50 55 60 65 70 75 80
diffCP
diffHB
diffVD
Multiple Comparison Test Plot, AAA7
No groups have mean ranks significantly different from diffCP
Figure 22: AAA7 Multiple Comparisons Test
75
0 2 4 6 8 10 12 14 16 18 200
50
100
150
segment #
ave
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s
Average Absolute Differences between Visual and Computer Estimates, AAA8
Wavelet denoising + Thresholding
Thresholding
Change-point analysis
Figure 23: AAA8 Average Absolute Differences
Table 14: AAA8 Kruskal-Wallis ANOVA
15 20 25 30 35 40 45
diffCP
diffHB
diffVD
Multiple Comparisons Test Plot, AAA8
No groups have mean ranks significantly different from diffCP
Figure 24: AAA8 Multiple Comparisons Test
76
0 5 10 15 20 25 30 35 400
50
100
150
200
250
300
350
400
450
500
segment #
ave
rage
ab
solu
te d
iffe
ren
ce m
illise
con
ds
Average Absolute Differences between Visual and Computer Estimates, AAA9
Wavelet denoising + Thresholding
Thresholding
Change-point analysis
Figure 25: AAA9 Average Absolute Differences
Table 15: AAA9 Kruskal-Wallis ANOVA
20 30 40 50 60 70 80
diffCP
diffHB
diffVD
Multiple Comparisons Test Plot, AAA9
2 groups have mean ranks significantly different from diffCP
Figure 26: AAA9 Multiple Comparisons Test
77
Appendix F: Average Absolute Differences Plots, Kruskal-Wallis / ANOVA
Tables and Multiple Comparisons Plots for Trunk Muscle EMG
0 10 20 30 40 50 60 700
50
100
150
200
250
300
segment #
avera
ge a
bsolu
te d
iffe
rence
milliseco
nds
Average Absolute Differences between Visual and Computer Estimates, KM
Wavelet denoising + Thresholding
Thresholding
Change-point analysis
Figure 27: Subject 1 Average Absolute Differences
Table 16: Subject 1 Kruskal-Wallis ANOVA
80 85 90 95 100 105 110
diffCP
diffHB
diffVD
Multiple Comparisons Test Plot, KM
No groups have mean ranks significantly different from diffCP
Figure 28: Subject 1 Multiple Comparisons Test
78
0 5 10 15 20 25 30 35 40 450
100
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300
400
500
600
segment #
ave
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Average Absolute Differences between Visual and Computer Estimates, NK
Wavelet denoising + Thresholding
Thresholding
Change-point analysis
Figure 29: Subject 2 Average Absolute Differences
Table 17: Subject 2 Kruskal-Wallis ANOVA
40 50 60 70 80 90 100
diffCP
diffHB
diffVD
Multiple Comparisons Test Plot, NK
2 groups have mean ranks significantly different from diffCP
Figure 30: Subject 2 Multiple Comparisons Test
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