Kernel machine-based one-parameter regularized Fisher discriminant method for face recognition

This paper addresses two problems in linear discriminant analysis (LDA) of face recognition. The first one is the problem of recognition of human faces under pose and illumination variations. It is well known that the distribution of face images with different pose, illumination, and face expression is complex and nonlinear. The traditional linear methods, such as LDA, will not give a satisfactory performance. The second problem is the small sample size (S3) problem. This problem occurs when the number of training samples is smaller than the dimensionality of feature vector. In turn, the within-class scatter matrix will become singular. To overcome these limitations, this paper proposes a new kernel machine-based one-parameter regularized Fisher discriminant (K1PRFD) technique. K1PRFD is developed based on our previously developed one-parameter regularized discriminant analysis method and the well-known kernel approach. Therefore, K1PRFD consists of two parameters, namely the regularization parameter and kernel parameter. This paper further proposes a new method to determine the optimal kernel parameter in RBF kernel and regularized parameter in within-class scatter matrix simultaneously based on the conjugate gradient method. Three databases, namely FERET, Yale Group B, and CMU PIE, are selected for evaluation. The results are encouraging. Comparing with the existing LDA-based methods, the proposed method gives superior results.

I. Introduction

Face recognition research started in the late 1970s and has become one of the most active and exciting research areas in computer science and information technology since 1990. A number of algorithms/techniques have been developed in the last decade. Two very good reviews can be found in [1] and [2]. Among various techniques, the linear (Fisher) discriminant analysis (LDA) based [3] method is one of the promising approaches in face recognition. LDA is theoretically sound and its objective is to find the most discriminant feature for classification. Therefore, it is good for pattern recognition problem. The first well-known LDA-based face recognition algorithm, Fisherface [3], was reported in 1997. After that, a number of LDA-based face recognition algorithms/systems are then developed. In general, LDA-based face recognition algorithm gives a good result under controlled conditions.