Abstract

In many vision problems, the observed data lies in a nonlin- ear manifold in a high-dimensional space. This paper presents a generic modelling scheme to characterize the nonlinear structure of the manifold and to learn its multimodal distribution. Our approach represents the data as a linear combination of parameterized local components, where the statistics of the component parameterization describe the nonlinear structure of the manifold. The components are adaptively selected from the training data through a progressive density approximation proce- dure, which leads to the maximum likelihood estimate of the underlying density. We show results on both synthetic and real training sets, and demonstrate that the proposed scheme has the ability to reveal impor- tant structures of the data.