Generalized Local Discriminant Embedding for Face Recognition

Abstract

Local Discriminant Embedding (LDE) was recently proposed to overcome some limitations of the global Linear Discriminant Analysis (LDA) method. In the case of a small training data set, however, LDE cannot directly be applied to high-dimensional data. This case is the so-called small-sample-size (SSS) problem. In this paper, we introduce an Exponential Local Discriminant Embedding (ELDE) technique to overcome the SSS problem. The advantages of ELDE are that, compared with Principal Component Analysis (PCA) + LDE, the ELDE method can extract the most discriminant information that was contained in the null space of the locality preserving between-class and within-class scatter matrices. In addition, the proposed ELDE is equivalent to transforming original data into a new space by distance diffusion mapping, and then, LDE is applied in such a new space. As a result of diffusion mapping, the margin between samples belonging to different classes is enlarged, which is helpful in improving classification accuracy. The experiments are conducted on four public face databases, YALE, PIE, Extended Yale and PF01. Experiments conducted on real data show that the performance of ELDE is better than that of LDE and many state-of-the-art discriminant analysis techniques.