Calibrated model-based evidential clustering using bootstrapping

TL;DR

This paper introduces a bootstrapping-based method for evidential clustering that constructs calibrated belief functions, ensuring the belief-plausibility intervals reliably contain true pairwise probabilities with a specified confidence level.

Contribution

The paper presents a novel approach combining bootstrapping with evidential clustering to produce calibrated belief functions with frequentist guarantees.

Findings

Method achieves calibration with confidence levels verified by simulation.

Effective on real datasets demonstrating practical applicability.

Provides a new way to quantify uncertainty in clustering results.

Abstract

Evidential clustering is an approach to clustering in which cluster-membership uncertainty is represented by a collection of Dempster-Shafer mass functions forming an evidential partition. In this paper, we propose to construct these mass functions by bootstrapping finite mixture models. In the first step, we compute bootstrap percentile confidence intervals for all pairwise probabilities (the probabilities for any two objects to belong to the same class). We then construct an evidential partition such that the pairwise belief and plausibility degrees approximate the bounds of the confidence intervals. This evidential partition is calibrated, in the sense that the pairwise belief-plausibility intervals contain the true probabilities "most of the time", i.e., with a probability close to the defined confidence level. This frequentist property is verified by simulation, and the practical applicability of the method is demonstrated using several real datasets.