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![Page 1: A New Temporal Pattern Identification Method for Characterization and Prediction of Complex Time Series Events Advisor : Dr. Hsu Graduate : You-Cheng Chen.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bf781a28abf838c81fac/html5/thumbnails/1.jpg)
A New Temporal Pattern Identification Method for
Characterization and Prediction of Complex Time Series Events
Advisor : Dr. HsuGraduate : You-Cheng ChenAuthor : Richard J Povinelli Xin Feng
![Page 2: A New Temporal Pattern Identification Method for Characterization and Prediction of Complex Time Series Events Advisor : Dr. Hsu Graduate : You-Cheng Chen.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bf781a28abf838c81fac/html5/thumbnails/2.jpg)
Motivation Objective Introduction Fundamental Concepts Framework of The Method Application Conclusions Personal Opinion
Outline
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Motivation
Many of the significant temporal patternsare unobvious, contaminated with noise,hence ,are difficult to identify usingtraditional time series analysis methods.
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Objective
To propose a method for identification of temporal patterns that characterize the events of interest in the time series.
![Page 5: A New Temporal Pattern Identification Method for Characterization and Prediction of Complex Time Series Events Advisor : Dr. Hsu Graduate : You-Cheng Chen.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bf781a28abf838c81fac/html5/thumbnails/5.jpg)
Introduction
Fig 1. Synthetic seismic time series with events
![Page 6: A New Temporal Pattern Identification Method for Characterization and Prediction of Complex Time Series Events Advisor : Dr. Hsu Graduate : You-Cheng Chen.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bf781a28abf838c81fac/html5/thumbnails/6.jpg)
Introduction
Outline of the Proposed Method
},...,1,{ NtxX t
Using time-delayed embedding unfold time series X into IRQ
- a reconstructed phase space.
A set of Q time series observations taken from X map to
Step A
},,,{ ,2)1( tTtTtTQt xxxx
TtTtTtTQtt xxxx ),,,(x ,2)1(
![Page 7: A New Temporal Pattern Identification Method for Characterization and Prediction of Complex Time Series Events Advisor : Dr. Hsu Graduate : You-Cheng Chen.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bf781a28abf838c81fac/html5/thumbnails/7.jpg)
Introduction
Step B
Event characterization function g(xt) is associated witheach phase space point xt
g(xt) represents the value of future “eventness” for thephase space point xt
![Page 8: A New Temporal Pattern Identification Method for Characterization and Prediction of Complex Time Series Events Advisor : Dr. Hsu Graduate : You-Cheng Chen.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bf781a28abf838c81fac/html5/thumbnails/8.jpg)
Temporal pattern cluster P is defined as a ball consisting ofall points within a certain distance Ď of a temporal patternp in the IRQ
Construct a heterogeneous collection of temporal patternclusters C*, such that C* is the optimizer of the objectivefunction f.
Introduction
Step C
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Fundamental Concepts
Because of noise, the temporal pattern does not perfectly match the time series observations that precede events. To overcome this limitation, a temporal pattern cluster is employed to capture the variability of a temporal pattern.
Temporal Pattern Cluster
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Fundamental Concepts
},,,{ ,2)1( tTtTtTQt xxxx The observationscan be compared to a temporal pattern.
Temporal patterns and events are placed into three categories: past, present, and future.
Temporal Pattern & Event
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Fundamental Concepts
Time-Delay Embedding
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Fundamental Concepts
Event Characterization FunctionIn order to correlate a temporal pattern with an event,the event characterization function g(xt) is introduced.
1t )(x txg
3t )(x txg
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The augmented phase space is a Q+1 dimensionalspace formed by extending the phase space with g(*)as the extra dimension. ex < xt,g(xt) >
Fundamental Concepts
Augmented Phase Space
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Fundamental Concepts
Object Function
The object function represents the efficacy of a collection of temporal pattern clusters to characterize events.
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Three example object function
Fundamental Concepts
The first object function is the t-test for the differencebetween two independent means and is useful foridentifying a single temporal pattern.
)()(
)(22
QcPc
uuPf
qp
qp
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Fundamental Concepts
The second objective function is useful for finding a single temporal pattern cluster that minimizes the incorrect positive predictions.
fptp
tpPf
)(
![Page 17: A New Temporal Pattern Identification Method for Characterization and Prediction of Complex Time Series Events Advisor : Dr. Hsu Graduate : You-Cheng Chen.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bf781a28abf838c81fac/html5/thumbnails/17.jpg)
Fundamental Concepts
The third objective function is useful for maximize Characterization/Prediction accuracy.
fnfptntp
tntpCf
)(
![Page 18: A New Temporal Pattern Identification Method for Characterization and Prediction of Complex Time Series Events Advisor : Dr. Hsu Graduate : You-Cheng Chen.](https://reader035.fdocuments.us/reader035/viewer/2022062409/5697bf781a28abf838c81fac/html5/thumbnails/18.jpg)
Framework of The Method
Diagram of Algorithm
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Framework of The Method
An Example for training Stages
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Framework of The Method
Step 1-Model the Goal
The event characterization function is g(Xt)=Xt+1
The objective function is
)()(
)(22
QcPc
uuPf
qp
qp
Step 2-Determize Temporal Pattern Length
The value of Q, i.e., the length of the temporal pattern
and the dimension of the phase space.Here we set Q=2, which allows a graphical presentationof the phase space.
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Framework of The Method
Step 3-Unfold the Training Time Series into thePhase Space.
The Manhattan distanceGiven two points y and z in IRQ, the distance between the two points is
Q
iii zyzyd
1
),(
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Step 3-Unfold the Training Time Series into thePhase Space.
Framework of The Method
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Framework of The Method
Step 4-Form Augmented Phase Space.
Augmenting the phase space with the extra dimension g(*)
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Framework of The Method
Step 6-Search for Optimal Temporal Pattern Cluster.
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Application-Welding Droplet Releases
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Application-Welding Droplet ReleasesSamples of these time series
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Application-Welding Droplet Releases
The stickout time series is preprocessed to remove thelarge-scale artifact.
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Application-Welding Droplet Releases
The event characterization function is g(Xt)=Xt+1
The objective function for the collection of temporalpattern clusters is
fnfptntp
tntpCf
)(
The range of phase space dimensions Q is [1,20]
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Application-Welding Droplet Releases
Recalibrated stickout time series (testing)
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Application-Welding Droplet Releases
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Conclusions
The paper has presented the new frameworkincluding the key concept of event characterizationfunction, temporal pattern clusters, time-delay embedding,augmented phase space, and objective function.
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Personal OpinionThe event function that characterizes one to fivetime steps ahead instead of in just one time step ahead may can be employed to improve accuracyand performance.