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adfa, p. 1, 2011.

© Springer-Verlag Berlin Heidelberg 2011

Null Space Diversity Fisher Discriminant Analysis for

Face Recognition

Xingzhu LIANG

a

, Yu’e LIN

b

, Gaoming YANG

c

, Guangyu XU

d

School of Computer Science and Engineering, Anhui University of Science and

Technology

Huainan, 232001, China

a

lxz9117@126.com,

b

linyu_e@126.com,

c

gmyang@aust.edu.cn,

d

gyxu@aust.edu.cn

Abstract.

The feature extraction algorithms, which attempt to project the original data in-

to a lower dimensional feature space , have drawn much attention. In this paper,

based on enhanced fisher discriminant criterion (EFDC), a new feature extrac-

tion method called null space diversity fisher discriminant analysis (NSDFDA)

is proposed for face recognition. NSDFDA based on a new optimization criteri-

on is presented, which means that all the discriminant vectors can be calculated

in the null space of the within-class scatter. Moreover, the proposed algorithm is

able to extract the orthogonal discriminant vectors in the feature space and sim-

ultaneously does not suffer from the small sample size problem, which is desir-

able for many pattern analysis applications. Experimental results on the Yale da-

tabase show the effectiveness of the proposed method.

Keywords: feature extraction, enhanced fisher discriminant criterion, null

space, the within-class scatter, the small sample size problems

1 Introduction

The feature extraction is a critical issue in face recognition tasks. The goal of fea-

ture extraction is to map high dimensional data samples to a lower dimensional space

such that certain properties are preserved. Among all the dimensionality reduction

methods, Fisher linear discriminant analysis (FLDA)[1] is the most popular method

and has been widely used in many classification applications. FLDA seeks to find

directions on which the ratio of the trace of the between-class matrix and the trace of

the within-class matrix is maximized. However, some recent research shows that the

samples may reside on a nonlinear submanifold. FLDA fails to discover the underly-

ing submanifold structure, due to the fact that it aims only to preserve the global

structures of the samples. Another technique called Locality Preserving Projections

(LPP) [2] has been proposed for dimensionality reduction, which can preserve the

intrinsic geometry of data. However, LPP has no direct relationship to classification.

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