Manifold Clustering

Abstract

Manifold learning has become a vital tool in data driven methods for interpretation of video, motion capture, and handwritten character data when they lie on a low dimensional, nonlinear manifold. This work extends manifold learning to classify and parameterize unlabeled data which lie on multiple, intersecting manifolds. This approach significantly increases the domain to which manifold learning methods can be applied, allowing parameterization of example manifolds such as figure eights and intersecting paths which are quite common in natural data sets. This approach introduces several technical contributions which may be of broader interest, including node-weighted multidimensional scaling and a fast algorithm for weighted low-rank approximation for rank-one weight matrices. We show examples for intersecting manifolds of mixed topology and dimension and demonstrations on human motion capture data.