Discriminant Analysis for Biometric Recognition

Discriminant Analysis for Biometric Recognition

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.ch002
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Abstract

This chapter is a brief introduction to biometric discriminant analysis technologies — Section I of the book. Section 2.1 describes two kinds of linear discriminant analysis (LDA) approaches: classification-oriented LDA and feature extraction-oriented LDA. Section 2.2 discusses LDA for solving the small sample size (SSS) pattern recognition problems. Section 2.3 shows the organization of Section I.
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Linear Discriminant Analysis

Linear discriminant analysis (LDA) method has been widely studied in and successfully applied to biometric recognition such as face, fingerprint, and palm print identification or verification.

The essence of LDA is to construct a linear discriminant criterion which can be used to build a binary classifier or a feature extractor. To differentiate LDA for binary classification from LDA for feature extraction, hereafter we name the former as classification-oriented LDA, and the later feature extraction-oriented LDA.

Classification-Oriented Linear Discriminant Analysis

Linear discriminant analysis was initially developed for binary classification in the seminal work of LDA (Fisher, 1936). Among various discriminant criteria, one of the most famous is Fisher discriminant criterion (FDC) for binary linear discriminant analysis. FDC tries to seek an optimal projection direction such that the between-class variance is maximized while the within-class variance is minimized if samples from two distinct classes are projected along this projection direction. Besides FDC, there exist other linear discriminant criteria for binary classification. Among them, perceptron and minimum squared-error (MSE) (Duda, Hart, & Stork, 2001) criteria are two well-known examples.

The mathematical form of each linear discriminant criterion can be characterized as an optimization model which is used to calculate the weight and sometimes the bias of a binary classifier. Similarly, the mathematical form of linear support vector machine (LSVM) (Burges, 1998) is also an optimization model to calculate the weight and bias for a binary classifier. Thus, LSVM can be viewed as a kind of classification-oriented LDA method.

Classification-oriented LDA methods are in fact binary linear classifiers and can not directly be applied to multiple pattern classification tasks. They should be used in combination with one of the implementation strategies described in Section 3.1.3 if they are applied to these tasks.

Feature Extraction-Oriented Linear Discriminant Analysis

Based on Fisher’s work, Wilks (1962) extended the concept of optimal projection direction to a set of discriminant vectors by extending Fisher discriminant criterion to multiple Fisher discriminant criterion. While the former is used to calculate the weight of the Fisher classifier, the latter is used to compute a set of Fisher discriminant vectors. By using these discriminant vectors as a transformation matrix, Wilks successfully reduced a complicated classification problem in a high-dimensional input space into a simple one in a low-dimensional feature space. The procedure which compresses the data from the input space into a feature space by utilizing a transformation matrix is called linear feature extraction. The feature extraction method using Fisher discriminant vectors is called Fisher linear discriminant (FLD).

In general, Fisher discriminant vectors are unnecessarily orthogonal to each other. Many researchers believed that the discriminant capability of FLD could be enhanced by removal of linear dependence among Fisher discriminant vectors. Based on this intuition, Foley-Sammon discriminant (FSD) — a feature extraction method which used a set of orthogonal discriminant vectors was subsequently developed (Sammon, 1970; Foley & Sammon, 1975; Duchene & Leclercq, 1988).

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Lda For Solving The Small Sample Size Problems

The Small Sample Size Pattern Recognition Problems

Since FDC, MSE, FLD, and FSD all involve the computation of the inverse of one or several scatter matrices of sample data, it is a precondition that these matrices should be nonsingular. In the small sample size (SSS) pattern recognition problems such as appearance-based face recognition, the ratio of dimensionality of input space to the number of samples is so large that the matrices involved are all singular. As a result, standard LDA methods cannot directly be applied to these SSS problems. Due to the prospective applications to biometric identification and computer vision, LDA for solving the SSS problems becomes one of the hottest research topics in pattern recognition.

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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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