Exploring and Understanding the High Dimensional and Sparse Image Face Space: a Self-Organized Manifold Mapping

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Face recognition has motivated several research studies in the last years owing not only to its applicability and multidisciplinary inherent characteristics, but also to its important role in human relationship. Despite extensive studies on face recognition, a number of related problems has still remained challenging in this research topic. It is well known that humans can overcome any computer program in the task of face recognition when artefacts are present such as changes in pose, illumination, occlusion, aging and etc. For instance, young children can robustly identify their parents, friends and common social groups without any previous explicit teaching or learning. Some recent research in Neuroscience (Kandel et al., 2000; Bakker et al., 2008) has shown that there is some new information about how humans deal with such high dimensional and sparse visual recognition task, indicating that the brain does not memorize all details of the visual stimuli (images) to perform face recognition (Brady et al., 2008). Instead, our associative memory tends to work essentially on the most expressive information (Bakker et al., 2008; Oja, 1982). In fact, theoretical models (Treves and Rolls, 1994; O’Reilly and Rudy, 2001; Norman and O’Reilly, 2003) have 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 (O’Reily and McClelland, 1994; Kuhl et al., 2010). Therefore, subspace learning techniques have a close biological inspiration and reasonability in terms of computational methods to possibly exploring and understanding the human behaviour of recognizing faces. The aim of this chapter is to study the non-supervised subspace learning called SelfOrganizing Map (SOM) (Kohonen, 1982; Kohonen, 1990) based on the principle of prototyping face image observations. Our idea with this study is not only to seek a low dimensional Euclidean embedding subspace of a set of face samples that describes the intrinsic similarities of the data (Kitani et al., 2006; Giraldi et al., 2008; Thomaz et al., 2009; Kitani et al., 2010), but also to explore an alternative mapping representation based on manifold models topologically constrained.