Comments on "Iteratively Re-weighted Algorithm for Fuzzy c-Means"
This is an incremental improvement for researchers in clustering algorithms, simplifying an existing method without introducing new performance gains.
The authors tackled the complexity of the IRW-FCM algorithm for Fuzzy c-Means by providing a simpler derivation using the Majorization Minimization (MM) algorithm, which eliminates the inner loop and speeds up the algorithm as a single-loop version.
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.