A Spatial Regularization of LDA for Face Recognition

Abstract

This paper proposes a new spatial regularization of Fisher linear discriminant analysis (LDA) to reduce the overfitting due to small size sample (SSS) problem in face recognition. Many regularized LDAs have been proposed to alleviate the overfitting by regularizing an estimate of the within-class scatter matrix. Spatial regularization methods have been suggested that make the discriminant vectors spatially smooth, leading to mitigation of the overfitting. As a generalized version of the spatially regularized LDA, the proposed regularized LDA utilizes the non-uniformity of spatial correlation structures in face images in adding a spatial smoothness constraint into an LDA framework. The region-dependent spatial regularization is advantageous for capturing the non-flat spatial correlation structure within face image as well as obtaining a spatially smooth projection of LDA. Experimental results on public face databases such as ORL and CMU PIE show that the proposed regularized LDA performs well especially when the number of training images per individual is quite small, compared with other regularized LDAs.

Photon-counting linear discriminant analysis for face recognition at a distance

“…It is challenging to classify a facial image acquired in an uncontrolled setting like long distance. Various classifiers have been developed on the basis of statistical analyses [1][2][3][4][5][6][7][8][9]. Among them, Fisher Linear discriminant analysis (LDA) is a popular technique because it enables the maximization of the discrimination capability through the Fisher criterion [10].…”

“…The SSS problem occurs in most practical cases, when the number of pixels is larger than the number of available training images. Several approaches have been applied to overcome this problem, including dimensionality reduction using principal component analysis (PCA) [3,4], regularized LDA methods [5,6], and replacement of the inverse of the within-class matrix with a pseudo-inverse matrix [7]. However, these approaches cannot ensure the optimality of the Fisher criterion.…”