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.
翻译:在本评论中,我们提出了一个简单替代的引文,作为“Fuzzy c-Means” Fuzzy c-Means 问题的“Fuzzy c-Means 临时再加权算法” 中显示的RW-FM 运算法的替代引文。我们显示,为IRW-FM 算法所得出的迭代步骤只不过是大众化的MMM 最小化算法的步骤。本说明中显示的引文简单易懂,与IMW-FM 的衍生法不同,这里的衍生法并不包含任何辅助变量。此外,通过显示IMW-FM 算法的步骤,可以消除RW-FM 算法的内部循环,而算法可以有效地作为“ Singloc” 算法运行。更准确地说,基于MM的新的引文推断,即IMW-FC 单个内部循环足以减少模糊 c- means 客观功能,加快了IMW-FC 算法的速度。