Tensor Independent Component Analysis and Tensor Non-Negative Factorization

Tensor Independent Component Analysis and Tensor Non-Negative Factorization

David Zhang (Hong Kong Polytechnic University, Hong Kong), Fengxi Song (New Star Research Institute Of Applied Technology, China), Yong Xu (Harbin Institute of Technology, China) and Zhizhen Liang (Shanghai Jiao Tong University, China)
DOI: 10.4018/978-1-60566-200-8.ch010
OnDemand PDF Download:
$37.50

Abstract

In this chapter, we describe two tensor-based subspace analysis approaches (tensor ICA and tensor NMF) that can be used in many fields like face recognition and other biometric recognition. Section 10.1 gives the background and development of the two tensor-based subspace analysis approaches. Section 10.2 introduces tensor independent component analysis. Section 10.3 presents tensor nonnegative factorization. Section 10.4 discusses some potential applications of these two subspace analysis approaches in biometrics. Finally, we summarize this chapter in Section 10.5.
Chapter Preview
Top

Introduction

Independent component analysis (ICA) (Hyvärinen & Oja, 2001) is a statistical signal processing technique. The basic idea of ICA is to represent a set of random variables using basis functions, where the components are statistically independent or as independent as possible. In general, there are two arguments for using ICA for image representation and recognition. First, the high-order relationships among images pixels may contain important information for recognition tasks. Second, ICA seeks to find the directions so that the projections of the data into those directions have maximally non-Gaussian distribution, which may be useful for classification tasks. In addition, the concept of ICA can be viewed as a generalization of PCA, since it is concerned not only with the second-order dependencies between variables but also with high-order dependencies between them.

During the past several years, the ICA algorithm has been widely used in face recognition and biomedical data. Bartlett and Sejnowski (1997) have demonstrated that the recognition accuracy using ICA basis vectors is higher than that of the PCA basis vectors with 200 face images. They found that the ICA representation of faces has the invariance to big changes in pose and small changes in illuminations. In Bartlett, Movellan and Sejnowski (2002), the authors first organized the database into a matrix X where each row vector is a different image. In this representation, the images are random variables and the pixels are trials. In this case, it makes sense to talk about independence of images or functions of images. Two images i and j are independent if when moving across pixels. In addition, they transposed the matrix X and organized the data so that images are in the columns of X. In this representation, pixels are random variables and images are trials. Here, it also makes sense to talk about independence of pixels or functions of pixels. For example, pixel and would be independent if when moving across the entire set of images. Based on these two ideas, they suggested two ICA architectures (ICA Architectures I and II) for face representation and used the Infomax algorithm (Bell & Sejnowski, 1995, 1997) to implement ICA. Both architectures were evaluated on a subset of the FERET face database and were found to be effective for face recognition. Yuen and Lai (2000, 2002) adopted the fixed-point algorithm to obtain the independent components (ICs) and used a householder transform to gain the least square solution of a face image for representations. Liu and Wechsler (1999, 2003) used an ICA algorithm to perform ICA and assessed its performance for face identification. All of these researchers claimed that ICA outperforms PCA in face recognition. Other researchers, however, reported differently. Baek, Draper, Beveridge, and She (2002) reported that PCA outperforms ICA while Moghaddam (2002), Jin and Davoine (2004) reported no significant performance difference between the two methods. Socolinsky and Selinger (2002) reported that ICA outperforms PCA on visible images but PCA outperforms ICA on infrared images.

Complete Chapter List

Search this Book:
Reset
Table of Contents
Acknowledgment
Chapter 1
Overview  (pages 1-23)
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
A biometric system can be regarded as a pattern recognition system. In this chapter, we discuss two advanced pattern recognition technologies for... Sample PDF
Overview
$37.50
Chapter 2
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
This chapter is a brief introduction to biometric discriminant analysis technologies — Section I of the book. Section 2.1 describes two kinds of... Sample PDF
Discriminant Analysis for Biometric Recognition
$37.50
Chapter 3
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
As mentioned in Chapter II, there are two kinds of LDA approaches: classification- oriented LDA and feature extraction-oriented LDA. In most... Sample PDF
Discriminant Criteria for Pattern Classification
$37.50
Chapter 4
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
In this chapter, we first give a brief introduction to Fisher linear discriminant, Foley- Sammon discriminant, orthogonal component discriminant... Sample PDF
Orthogonal Discriminant Analysis Methods
$37.50
Chapter 5
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
In this chapter, we mainly present three kinds of weighted LDA methods. In Sections 5.1, 5.2 and 5.3, we respectively present parameterized direct... Sample PDF
Parameterized Discriminant Analysis Methods
$37.50
Chapter 6
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
In this chapter, we introduce two novel facial feature extraction methods. The first is multiple maximum scatter difference (MMSD) which is an... Sample PDF
Two Novel Facial Feature Extraction Methods
$37.50
Chapter 7
Tensor Space  (pages 135-149)
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
In this chapter, we first give the background materials for developing tensor discrimination technologies in Section 7.1. Section 7.2 introduces... Sample PDF
Tensor Space
$37.50
Chapter 8
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
Tensor principal component analysis (PCA) is an effective method for data reconstruction and recognition. In this chapter, some variants of... Sample PDF
Tensor Principal Component Analysis
$37.50
Chapter 9
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
Linear discriminant analysis is a very effective and important method for feature extraction. In general, image matrices are often transformed into... Sample PDF
Tensor Linear Discriminant Analysis
$37.50
Chapter 10
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
In this chapter, we describe two tensor-based subspace analysis approaches (tensor ICA and tensor NMF) that can be used in many fields like face... Sample PDF
Tensor Independent Component Analysis and Tensor Non-Negative Factorization
$37.50
Chapter 11
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
In this chapter, we describe tensor-based classifiers, tensor canonical correlation analysis and tensor partial least squares, which can be used in... Sample PDF
Other Tensor Analysis and Further Direction
$37.50
Chapter 12
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
In the past decades while biometrics attracts increasing attention of researchers, people also have found that the biometric system using a single... Sample PDF
From Single Biometrics to Multi-Biometrics
$37.50
Chapter 13
Feature Level Fusion  (pages 273-304)
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
This chapter introduces the basis of feature level fusion and presents two feature level fusion examples. As the beginning, Section 13.1 provides an... Sample PDF
Feature Level Fusion
$37.50
Chapter 14
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
With this chapter we aims at describing several basic aspects of matching score level fusion. Section 14.1 provides a description of basic... Sample PDF
Matching Score Level Fusion
$37.50
Chapter 15
Decision Level Fusion  (pages 328-348)
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
With this chapter, we first present a variety of decision level fusion rules and classifier selection approaches, and then show a case study of face... Sample PDF
Decision Level Fusion
$37.50
Chapter 16
Book Summary  (pages 349-358)
David Zhang, Fengxi Song, Yong Xu, Zhizhen Liang
With the title “Advanced Pattern Recognition Technologies with Applications to Biometrics” this book mainly focuses on two kinds of advanced... Sample PDF
Book Summary
$37.50
About the Authors