Dempster-Shafer clustering using Potts spin mean field theory

TL;DR

This paper introduces a computationally efficient method for clustering evidence in Dempster-Shafer theory by mapping the problem to an antiferromagnetic Potts spin model, enabling large-scale solutions.

Contribution

It presents a novel approximation that linearizes the conflict weight, maps it to a Potts model, and demonstrates improved scalability for evidence clustering tasks.

Findings

Achieves near-optimal clustering with O(N^2 log^2 N) complexity.

Establishes an isomorphism between the Potts model and a graph optimization problem.

Provides a framework for efficient large-scale evidence clustering.

Abstract

In this article we investigate a problem within Dempster-Shafer theory where 2**q - 1 pieces of evidence are clustered into q clusters by minimizing a metaconflict function, or equivalently, by minimizing the sum of weight of conflict over all clusters. Previously one of us developed a method based on a Hopfield and Tank model. However, for very large problems we need a method with lower computational complexity. We demonstrate that the weight of conflict of evidence can, as an approximation, be linearized and mapped to an antiferromagnetic Potts Spin model. This facilitates efficient numerical solution, even for large problem sizes. Optimal or nearly optimal solutions are found for Dempster-Shafer clustering benchmark tests with a time complexity of approximately O(N**2 log**2 N). Furthermore, an isomorphism between the antiferromagnetic Potts spin model and a graph optimization problem is shown. The graph model has dynamic variables living on the links, which have a priori probabilities that are directly related to the pairwise conflict between pieces of evidence. Hence, the relations between three different models are shown.