Controling the number of focal elements

TL;DR

This paper introduces techniques to limit the number of focal elements in basic belief assignments, reducing computational complexity while preserving information, through matrix methods and adapted clustering algorithms.

Contribution

It presents novel methods to control focal element quantity in belief functions, including matrix-based approaches and an adapted k-means clustering algorithm.

Findings

Reduced computational complexity in belief combination

Preservation of information with fewer focal elements

Effective clustering of focal elements using adapted k-means

Abstract

A basic belief assignment can have up to 2^n focal elements, and combining them with a simple conjunctive operator will need O(2^2n) operations. This article proposes some techniques to limit the size of the focal sets of the bbas to be combined while preserving a large part of the information they carry. The first section revisits some well-known definitions with an algorithmic point of vue. The second section proposes a matrix way of building the least committed isopignistic, and extends it to some other bodies of evidence. The third section adapts the k-means algorithm for an unsupervized clustering of the focal elements of a given bba.