PCM and APCM Revisited: An Uncertainty Perspective

TL;DR

This paper revisits PCM and APCM clustering algorithms from an uncertainty perspective, introducing new parameters and a unified framework that enhances control and understanding of the clustering process.

Contribution

It introduces a new uncertainty-based framework for PCM and APCM, incorporating parameters to better model and control clustering behavior, unifying their features.

Findings

Parameters $\sigma_v$ and $\alpha$ improve clustering control.

Unification of PCM and APCM features in the UPCM framework.

Experimental validation demonstrates enhanced flexibility and understanding.

Abstract

In this paper, we take a new look at the possibilistic c-means (PCM) and adaptive PCM (APCM) clustering algorithms from the perspective of uncertainty. This new perspective offers us insights into the clustering process, and also provides us greater degree of flexibility. We analyze the clustering behavior of PCM-based algorithms and introduce parameters $\sigma_v$ and $\alpha$ to characterize uncertainty of estimated bandwidth and noise level of the dataset respectively. Then uncertainty (fuzziness) of membership values caused by uncertainty of the estimated bandwidth parameter is modeled by a conditional fuzzy set, which is a new formulation of the type-2 fuzzy set. Experiments show that parameters $\sigma_v$ and $\alpha$ make the clustering process more easy to control, and main features of PCM and APCM are unified in this new clustering framework (UPCM). More specifically, UPCM reduces to PCM when we set a small $\alpha$ or a large $\sigma_v$, and UPCM reduces to APCM when clusters are confined in their physical clusters and possible cluster elimination are ensured. Finally we present further researches of this paper.