Classification of data on manifold.

Abstract

Data classification is one of the most challenging task in the field of pattern recognition and computer vision. Sometimes the values of signal or data are naturally described as points on a manifold. Such data arise from medial representations (m-reps) in medical images, Diffusion Tensor-MRI (DT-MRI), diffeomorphisms, etc. Since this may not be a vector space, one needs to be careful while choosing classification methods for such data. SVM is one of the popular methods which heavily relies on the fact that the underlying space is a vector space. In this thesis, we adapt SVM to classify data on manifold. We project data on the tangent space of a given manifold, which is a vector space and use SVM for classification on this vector space. We try to explore Euclidean SVM on multiple tangent planes so that we can generalize the idea of SVM for data on manifolds. We give an algorithm to find the point on whose tangent space the classification margin is maximized. We show results of classification with various manifolds like S2, SO(3) and PD(2). As computer vision application, we classify textures using SVM on PD(n) manifold.