Parameter Selections of Fuzzy C-Means Based on Robust Analysis

The weighting exponent m is called the fuzzifier that can have influence on the clustering performance of fuzzy c-means (FCM) and m∈ [1.5,2.5] is suggested by Pal and Bezdek [13]. In this paper, we will discuss the robust properties of FCM and show that the parameter m will have influence on the robustness of FCM. According to our analysis, we find that a large m value will make FCM more robust to noise and outliers. However, if m is larger than the theoretical upper bound proposed by Yu et al. [14], the sample mean will become the unique optimizer. Here, we suggest to implement the FCM algorithm with m∈ [1.5,4] under the restriction when m is smaller than the theoretical upper bound. Keywords—Fuzzy c-means, robust, fuzzifier.