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Orthogonal Discriminant Analysis Methods

Copyright © 2009. 20 pages.
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DOI: 10.4018/978-1-60566-200-8.ch004
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MLA

Zhang, David, Fengxi Song, Yong Xu and Zhizhen Liang. "Orthogonal Discriminant Analysis Methods." Advanced Pattern Recognition Technologies with Applications to Biometrics. IGI Global, 2009. 58-77. Web. 21 Oct. 2014. doi:10.4018/978-1-60566-200-8.ch004

APA

Zhang, D., Song, F., Xu, Y., & Liang, Z. (2009). Orthogonal Discriminant Analysis Methods. In D. Zhang, F. Song, Y. Xu, & Z. Liang (Eds.) Advanced Pattern Recognition Technologies with Applications to Biometrics (pp. 58-77). Hershey, PA: Medical Information Science Reference. doi:10.4018/978-1-60566-200-8.ch004

Chicago

Zhang, David, Fengxi Song, Yong Xu and Zhizhen Liang. "Orthogonal Discriminant Analysis Methods." In Advanced Pattern Recognition Technologies with Applications to Biometrics, ed. David Zhang, Fengxi Song, Yong Xu and Zhizhen Liang, 58-77 (2009), accessed October 21, 2014. doi:10.4018/978-1-60566-200-8.ch004

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Abstract

In this chapter, we first give a brief introduction to Fisher linear discriminant, Foley- Sammon discriminant, orthogonal component discriminant, and application strategies for solving the SSS problems. We then present two novel orthogonal discriminant analysis methods, orthogonalized Fisher discriminant and Fisher discriminant with Schur decomposition. At last, we compare the performance of several main orthogonal discriminant analysis methods under various SSS strategies.
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Introduction

Fisher Linear Discriminant

Fisher linear discriminant (FLD) (Duda, Hart, & Stork, 2001) operates by learning a discriminant matrix which maps a d-dimensional input space into an r-dimensional feature space by maximizing the multiple Fisher discriminant criterion.Specifically, a Fisher discriminant matrix is an optimal solution of the following optimization model:

. (1)

Here is an arbitrary matrix, and and are the between- and within- class scatter matrices, and is the determinant of a square matrix.

The between-class scatter matrix SB and the within-class scatter matrix SW are defined as follows,, (2) and

. (3)

Here Ni and are respectively the number and the mean of samples from the ith class , the mean of samples from all classes, and l the number of classes.

It has been proved that if is nonsingular, the matrix composed of unit eigenvectors of the matrix corresponding to the first r largest eigenvalues is an optimal solution of the optimization model defined in Eq. (1) (Wilks, 1962). The matrix is the Fisher discriminant matrix commonly used in Fisher linear discriminant.

Since the matrix is usually asymmetric, Fisher discriminant vectors, i.e. column vectors of the Fisher discriminant matrix are unnecessary orthogonal to each other.

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Complete Chapter List

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Table of Contents
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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