Regularized Kernel Locality Preserving Discriminant Analysis for Face Recognition - Advanced Concepts for Intelligent Vision Systems - page 283

Regularized Kernel Locality Preserving
Discriminant Analysis for Face Recognition

Xiaohua Gu, Weiguo Gong, Liping Yang, and Weihong Li

Laboratory of Optoelectronic Technology and Systems of the Education Ministry of
China, Chongqing University, Chongqing, 400044 China
{ xhgu,wggong,yanglp,weihongli } @cqu.edu.cn

Abstract. In this paper, a regularized kernel locality preserving
discriminant analysis (RKLPDA) method is proposed for facial feature
extraction and recognition. The proposed RKLPDA comes into the char-
acteristic of LPDA that encodes both the geometrical and discriminant
structure of the data manifold, and improves the classification ability
for linear non-separable data by introducing kernel trick. Meanwhile, by
regularizing the eigenvectors of the kernel locality preserving within-class
scatter, RKLPDA utilizes all the discriminant information and elimi-
nates the small sample size (SSS) problem. Experiments on ORL and
FERET face databases are performed to test and evaluate the proposed
algorithm. The results demonstrate the effectiveness of RKLPDA.

Keywords: Locality preserving discriminant analysis, Kernel method,
Feature extraction, Face recognition.

1 Introduction

Discriminant analysis is a technique of finding a transformation which character-
izes or separates two or more classes by maximizing the inter-class diversity and
meanwhile minimizing the intra-class compactness. Representative discriminant
analysis methods include linear discriminant analysis (LDA) [1], locality preserv-
ing discriminant analysis (LPDA) [2], and their null space extensions, null space
LDA (NLDA) [3], null space DLPP (NDLPP) [4] and etc.. LDA based methods,
which dwell on estimating the global statistics, fail to discover the underlying
structure if the data lie on or close to a sub-manifold embedding in the high-
dimensional input space. LPDA based methods, as the discriminant analysis
extensions of locality preserving projections (LPP)[5], encode both the geomet-
rical and discriminant structure of the data manifold and are more powerful.
However, when applied to face recognition, they may suffer from the following
problems: (1) Due to the high dimensionality of the sample space and the lim-
ited training samples, LDA and LPDA always suffer from the well-known SSS
problem; (2) The discriminative information resides in both the principal and
the null subspaces of intra-class compactness matrix [6]. Nevertheless, NLDA
and NLPDA extract only that in the null subspace; (3) For C -class recognition