Markov Random Walk Representations with Continuous Distributions

We propose a framework to extend Markov random walks (Szummer and Jaakkola, 2001) to a continuum of points. In this framework, the transition probability between two points is the integral of the probability density over all paths connecting the two points. Evaluation of this transition probability is equivalent to solving the diffusion equation with a potential term. The solution is a generalization to the heat kernel (Kondor and Lafferty, 2001; Belkin and Niyogi, 2002). The continuation of discrete random walks allows us to incorporate prior knowledge about the manifold shape and the distribution of data. Experiments on a synthetic dataset suggest that continuous random walks capture the distance metric on a manifold more faithfully than discrete random walks.

• Type: Conference
• Year: 2003
• Where: UAI
• Authors: Chen-Hsiang Yeang, Martin Szummer
• Keywords: Discrete Random Walks, Markov Random Walks, Random Walks, UAI 2003, UAI 2008