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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