Discriminant Component Analysis and Self-Organized Manifold Mapping for Exploring and Understanding Image Face Spaces

Face recognition is a multidisciplinary field that involves subjects in neuroscience, computer science and statistical learning. Some recent research in neuroscience has indicated that the ability of our memory relies on the capability of orthogonalizing (pattern separation) and completing (pattern prototyping) partial patterns in order to encode, store and recall information. From a computational viewpoint, pattern separation can be cast in the subspace learning area while pattern prototyping is closer to manifold learning methods. So, subspace (or manifold) learning techniques have a close biological inspiration and reasonability in terms of computational methods to possibly exploring and understanding the human behavior of recognizing faces. Therefore, the aim of this paper is threefold. Firstly, we review some theoretical aspects about perceptual and cognitive processes related to the mechanisms of pattern separation and pattern prototyping. Then, the paper presents the basic idea of manifold learning and its relationship with subspace learning with focus on the dimensionality reduction problem. Finally, we present the Discriminant Principal Component Analysis (DPCA) and the Self-Organized Manifold Mapping (SOMM) algorithm to exemplify respectively pattern separation and completion techniques. We show experimental results to demonstrate the effectiveness of DPCA and SOMM algorithms on well-framed face image analysis.