Dimensionality Reduction, Classification and Reconstruction Problems in Statistical Learning Approaches

Statistical learning theory explores ways of estimating functional dependency from a given collection of data. The specific sub-area of supervised statistical learning covers important models like Perceptron, Support Vector Machines (SVM) and Linear Discriminate Analysis (LDA). In this paper we firstly review the theory of such models. Then, we compare their separating hypersurfaces for extracting group-differences between images. Classification and reconstruction are the targets in this comparison. Next, we describe our idea of using the discriminant weights given by separating hyperplanes for discriminant features analysis and selection. Finally, we present experimental results on breast cancer classification and face images and discuss future works in this area.