Maximum neighborhood margin criterion in face recognition

Feature extraction is a data analysis technique devoted to removing redundancy and extracting the most discriminative information. In face recognition, feature extractors are normally plagued with small sample size problems, in which the total number of training images is much smaller than the image dimensionality. Recently, an optimized facial feature extractor, maximum marginal criterion (MMC), was proposed. MMC computes an optimized projection by solving the generalized eigenvalue problem in a standard form that is free from inverse matrix operation, and thus it does not suffer from the small sample size problem. However, MMC is essentially a linear projection technique that relies on facial image pixel intensity to compute within- and between-class scatters. The nonlinear nature of faces restricts the discrimination of MMC. Hence, we propose an improved MMC, namely maximum neighborhood margin criterion (MNMC). Unlike MMC, which preserves global geometric structures that do not perfectly describe the underlying face manifold, MNMC seeks a projection that preserves local geometric structures via neighborhood preservation. This objective function leads to the enhancement of classification capability, and this is testified by experimental results. MNMC shows its performance superiority compared to MMC, especially in pose, illumination, and expression (PIE) and face recognition grand challenge (FRGC) databases.