Diffusion Methods for Classification with Pairwise Relationships
This work addresses classification tasks with structured relationships, such as in computer vision, but appears incremental as it builds on existing message passing and diffusion methods.
The paper tackles classification problems with pairwise relationships by developing two diffusion-based algorithms that propagate information using contraction maps, guaranteeing convergence to unique fixed points on arbitrary graphs. The algorithms are applied to image restoration, stereo depth estimation, and binary classification on a grid, though no concrete performance numbers are provided.
We define two algorithms for propagating information in classification problems with pairwise relationships. The algorithms are based on contraction maps and are related to non-linear diffusion and random walks on graphs. The approach is also related to message passing algorithms, including belief propagation and mean field methods. The algorithms we describe are guaranteed to converge on graphs with arbitrary topology. Moreover they always converge to a unique fixed point, independent of initialization. We prove that the fixed points of the algorithms under consideration define lower-bounds on the energy function and the max-marginals of a Markov random field. The theoretical results also illustrate a relationship between message passing algorithms and value iteration for an infinite horizon Markov decision process. We illustrate the practical application of the algorithms under study with numerical experiments in image restoration, stereo depth estimation and binary classification on a grid.