Analysis of parameter selections for fuzzy c-means

The weighting exponent m is called the fuzzifier that can influence the performance of fuzzy c-means (FCM). It is generally suggested that m∈[1.5,2.5]. On the basis of a robust analysis of FCM, a new guideline for selecting the parameter m is proposed. We will show that a large m value will make FCM more robust to noise and outliers. However, considerably large m values that are greater than the theoretical upper bound will make the sample mean a unique optimizer. A simple and efficient method to avoid this unexpected case in fuzzy clustering is to assign a cluster core to each cluster. We will also discuss some clustering algorithms that extend FCM to contain the cluster cores in fuzzy clusters. For a large theoretical upper bound case, we suggest the implementation of the FCM with a suitable large m value. Otherwise, we suggest implementing the clustering methods with cluster cores. When the data set contains noise and outliers, the fuzzifier m=4 is recommended for both FCM and cluster-core-based methods in a large theoretical upper bound case.

► A new guideline for selecting the parameter m is proposed.
► A large m value will make FCM more robust to noise and outliers.
► A large theoretical upper bound FCM with m=4.
► A small theoretical upper bound FCM with cluster cores.