SUBSPACES VERSUS SUBMANIFOLDS: A COMPARATIVE STUDY IN SMALL SAMPLE SIZE PROBLEM

Abstract

Automatic face recognition is a challenging problem in the biometrics area, where the dimension of the sample space is typically larger than the number of samples in the training set and consequently the so-called small sample size problem exists. Recently, neuroscientists emphasized the manifold ways of perception, and showed the face images may reside on a nonlinear submanifold hidden in the image space. Many manifold learning methods, such as Isometric feature mapping, Locally Linear Embedding, and Locally Linear Coordination are proposed. These methods achieved the submanifold by collectively analyzing the overlapped local neighborhoods and all claimed to be superior to such subspace methods as Eigenfaces and Fisherfaces in terms of classification accuracy. However, in literature, no systematic comparative study for face recognition is performed among them. In this paper, we carry out a comparative study in face recognition among them, and the study considers theoretical aspects as well as simulations performed using CMU PIE and FERET face databases.