Exponential Local Discriminant Embedding and Its Application to Face Recognition

Local discriminant embedding (LDE) has been recently proposed to overcome some limitations of the global linear discriminant analysis 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. The classical solution to this problem was applying dimensionality reduction on the raw data (e.g., using principal component analysis). In this paper, we introduce a novel discriminant technique called "exponential LDE" (ELDE). The proposed ELDE can be seen as an extension of LDE framework in two directions. First, the proposed framework overcomes the SSS problem without discarding the discriminant information that was contained in the null space of the locality preserving scatter matrices associated with LDE. Second, the proposed ELDE is equivalent to transforming original data into a new space by distance diffusion mapping (similar to kernel-based nonlinear 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 five public face databases: Yale, Extended Yale, PF01, Pose, Illumination, and Expression (PIE), and Facial Recognition Technology (FERET). The results show that the performances of the proposed ELDE are better than those of LDE and many state-of-the-art discriminant analysis techniques.