A Statistical Discriminant Model for Face Interpretation and Reconstruction

Abstract

Abstract

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

“…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.…”

New Approaches to Characterization and Recognition of Faces

“…The aim of this chapter is to study the non-supervised subspace learning called Self-Organizing 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.…”

Dimensionality Reduction, Classification and Reconstruction Problems in Statistical Learning Approaches

“…Specifically, if we navigate on each principal component we observe that the most expressive components for reconstruction (i.e., the components with the largest eigenvalues) are not necessarily the most discriminant ones for classification. This can be seen as a special kind of the reconstruction problem and will be discussed using face images [19,31,18].…”

“…Such goal can be achieved through the separating hyperplanes generated by supervised statistical learning methods like Perceptron, SVM and LDA [32,14,13]. In the recent years, these methods have played an important role for characterizing differences between a reference group of patterns using image samples of patients [24,26,27,28,12] as well as face images [5,19,25,21]. Besides, their extensions for the non-linear case, as well as the Maximum uncertainty LDA (MLDA) approach to address the limited sample size problem, have been reported in a number of works in the literature [32,14,13,12,24,19,31,26,28,18].…”

“…We review the theory behind the cited methods, their common points, and discuss why SVM is in general the best technique for classification but not necessarily the best for extracting discriminant information. A case study of face recognition [31,19,25] will be used in order to help this discussion [20]. Moreover, such analysis points towards the idea of using the discriminant weights given by separating hyperplanes to select the most important features of a data set for classification.…”