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Transcript of 1synopsis tensor
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TENSOR DECOMPOSITION USING
TUCKER AND PARAFAC IN EEGSIGNAL
SYNOPSIS
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Problem Statement
Increasingly large amount of multidimensional data are being generated on a daily basis
in many applications. This leads to a strong demand for learning algorithms to extract usefulinformation from these massive data. Feature extraction and selection are key factors in model
reduction, classification and pattern recognition problems. This is especially important for inputdata with large dimensions such as brain recording or multiview images, where appropriate
feature extraction is a prerequisite to classification. To ensure that the reduced dataset containsmaximum information about input data we propose algorithms for feature extraction and
classification. This is achieved based on orthogonal or nonnegative tensor (multi-array)decompositions.
Introduction
Electrical impulses generated by nerve firings in the brain diffuse through the head and can be
measured by electrodes placed on the scalp, is known as electroencephalogram (EEG) and was
first measured in humans by Hans Berger in 1929. EEG is an important clinical tool for
diagnosing, monitoring and managing neurological disorders.
The analysis of EEG data and the extraction of information from this data is a difficult
problem. This problem is exacerbated by the introduction of extraneous biologically generated
and externally generated signals into the EEG. EEG data is used for development of brain-
computer interfaces (BCIs). The electroencephalogram (EEG), the record of the neuronal
electrical activity, is a good indicator of abnormality in the nervous central system.
Modern applications such as those in neuroscience, text mining, and pattern recognition generate
massive amounts of multimodel data exhibiting dimensionality. Tensors (i.e., multi-way arrays)
provide a natural representation for such data, and tensor decompositions and factorizations are
emerging as promising tools for exploratory analysis of multidimensional data. Tensor
decompositions, especially TUCKER and PARAFAC models, are important tools for feature
extraction and classification problems by capturing multi-linear and multi-aspect structures in
large-scale higher-order data-sets. There are a number of applications in diverse disciplines,
especially feature extraction, feature selection, classification and multi-way clustering [13].
Supervised and un-supervised dimensionality reduction and feature extraction methods with
tensor representation have recently attracted great interest [14]. Given that many real-world
data(e.g., brain signals, images, videos) are conveniently represented by tensors, traditional
algorithms such as PCA, LDA, and ICA could treat the data as matrices or vectors [58], and are
often not efficient. Since the curse of high dimensionality is often a major cause of limitation of
many practical methods, dimensionality reduction is a prerequisite to practical applications in
classification, data mining, vision and pattern recognitions fields.
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In classification and pattern recognition problems, there are three main stages: feature
extraction, feature selection, and classifier design. The key issue is to extract and select
statistically significant (dominant, leading) features, which allow us to discriminate different
classes or clusters. Classifier design involves choosing an appropriate method such as Fisher
discriminant analysis, k-nearest neighbor (KNN) rule, or support vector machines (SVM). In anutshell, the classifier computes distance or similarity among extracted features for training data
in order to assign the test data to specific class.
In this paper we propose a suite of algorithms for feature extraction and classification,
especially suitable for large scale problems. In our approach, we first decompose multi-way data
under the TUCKER decomposition with/without constraints to retrieve basis factors and
significant features from the core tensors.
Existing System
Diagram of the existing feature dimensionality reduction approach for EEG signal classification
is shown in Fig.1. In this approach, L-second epochs from EEG signals were decomposed by
Gabor function and represented in the spatial, spectral and temporal domain as third order
tensor. Then, a GTDA algorithm was developed to extract a multi-way discriminative subspace
from the third order tensors and form the optimal projection vector.
Figure 1. Block diagram of the existing feature dimensionality reduction approach.
EEG signals Divide each class to l-
section epoch
Feature extraction
based on GABOR
functions
Dimensionality reduction based on general tensor discriminant analysis
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Proposed System
In this paper we propose a suite of algorithms for feature extraction and classification, especially
suitable for large scale problems. In our approach, we first decompose multi-way data under the
TUCKER
decomposition with/without constraints to retrieve basis factors and significant features fromthe core tensors.
Figure2. Dimensional reduction..
Figure 3. Block diagram of the proposed feature dimensionality reduction approach.
EEG signals Divide each class to l-
section epoch
Feature extraction
based on GABOR
functions
Dimensionality reduction using TUCKER and PARAFAC and comparing
with the general method.
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PARAFAC
PARAFAC is one of several decomposition methods for multi-way data. PARAFAC is a
generalization of PCA to higher order arrays, but some of the characteristics of the method are
quite different from the ordinary two-way case.
TUCKER
TUCKER decomposition for a 3-way case, is a basic model for high dimensional tensors
which allows effectively to perform model reduction and feature extraction. In contrast with
PARAFAC, which decomposes a tensor into rank one tensor, the tucker decomposition is a form
of higher-order principal component analysis that decomposes a tensor into a core tensor
multiplied by a matrix along each mode.
Hardware and Software Requirements
Hardware Requirements
1. Intel Processor with minimum 20GB hard disk capacity.Operating System
1. Windows XP or windows 7 Operating SystemSoftware Requirements
1. Matlab 72. Tensor Toolkit
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References
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