论文标题
评论“迭代重新加权算法的模糊c均值”
Comments on "Iteratively Re-weighted Algorithm for Fuzzy c-Means"
论文作者
论文摘要
在此评论中，我们为模糊c均值问题的“迭代重新加权算法”中提出了一个简单的替代推导。我们表明，对于IRW-FCM算法而得出的迭代步骤不过是流行的多数化最小化（MM）算法的步骤。本说明中提出的派生更简单明了，与IRW-FCM的推导不同，此处的派生不涉及引入任何辅助变量。此外，通过将IRW-FCM的步骤显示为MM算法，可以消除IRW-FCM算法的内环，并且可以有效地作为“单个环”算法运行算法。更确切地说，新的基于MM的派生推断出IRW-FCM的单个内部环足足以降低模糊C均值的目标函数，从而加快了IRW-FCM算法的速度。
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.
