Comments on "Iteratively Re-weighted Algorithm for Fuzzy c-Means"
Abstract
In this comment, we present a simple alternate derivation to the IRW-FCM algorithm presented in "Iteratively Re-weighted Algorithm for Fuzzy c-Means" for Fuzzy c-Means problem. We show that the iterative steps derived for IRW-FCM algorithm are nothing but steps of the popular Majorization Minimization (MM) algorithm. The derivation presented in this note is much simpler and straightforward and, unlike the derivation of IRW-FCM, the derivation here does not involve introduction of any auxiliary variable. Moreover, by showing the steps of IRW-FCM as the MM algorithm, the inner loop of the IRW-FCM algorithm can be eliminated and the algorithm can be effectively run as a "single loop" algorithm. More precisely, the new MM-based derivation deduces that a single inner loop of IRW-FCM is sufficient to decrease the Fuzzy c-means objective function, which speeds up the IRW-FCM algorithm.
Cite
@article{arxiv.2209.07715,
title = {Comments on "Iteratively Re-weighted Algorithm for Fuzzy c-Means"},
author = {Astha Saini and Prabhu Babu},
journal= {arXiv preprint arXiv:2209.07715},
year = {2022}
}