# Diffusion Methods for Classification with Pairwise Relationships

arXiv: https://arxiv.org/abs/1505.06072 · HTML: https://mlsanity.com/paper/1505.06072/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2015.

## Built on by (most cited first, 1 of 1)

- [Convex Combination Belief Propagation Algorithms](https://mlsanity.com/paper/2105.12815/) (2021)

## Abstract (arXiv)

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.