On the convergence of the sparse possibilistic c-means algorithm

TL;DR

This paper provides a convergence proof for the sparse possibilistic c-means (SPCM) algorithm, demonstrating that its iterative process reliably converges to a stationary point, ensuring stability and reliability in clustering applications.

Contribution

The paper introduces a formal convergence proof for the SPCM algorithm using Zangwill's theorem, establishing theoretical guarantees for its convergence behavior.

Findings

SPCM algorithm's iterative sequence converges to a stationary point.

Convergence is guaranteed under the conditions specified in the proof.

A subsequence of the iterative process also converges to a stationary point.

Abstract

In this paper, a convergence proof for the recently proposed sparse possibilistic c-means (SPCM) algorithm is provided, utilizing the celebrated Zangwill convergence theorem. It is shown that the iterative sequence generated by SPCM converges to a stationary point or there exists a subsequence of it that converges to a stationary point of the cost function of the algorithm.