Manifold integration with markov random walks - Texas A&M University (TAMU) Scholar

Most manifold learning methods consider only one similarity matrix to induce a low-dimensional manifold embedded in data space. In practice, however, we often use multiple sensors at a time so that each sensory information yields different similarity matrix derived from the same objects. In such a case, manifold integration is a desirable task, combining these similarity matrices into a compromise matrix that faithfully reflects multiple sensory information. A small number of methods exists for manifold integration, including a method based on reproducing kernel Krein space (RKKS) or DISTA-TIS, where the former is restricted to the case of only two manifolds and the latter considers a linear combination of normalized similarity matrices as a compromise matrix. In this paper we present a new manifold integration method, Markov random walk on multiple manifolds (RAMS), which integrates transition probabilities defined on each manifold to compute a compromise matrix. Numerical experiments confirm that RAMS finds more informative manifolds with a desirable projection property. Copyright 2008, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.

Manifold integration with markov random walks Conference Paper