Plenary lecture 4: on robust fuzzy clustering and validity indexes
Miin‐Shen Yang · 2010
Cluster analysis is a method for finding clusters of a data set with the most similarity within the same cluster and the most dissimilarity between different clusters. It is unsupervised learning in pattern recognition. Since Zadeh [1] proposed fuzzy sets that introduced the idea of partial memberships described by the membership functions, fuzzy clustering has been widely studied and applied in a variety of substantive areas (see [2-5]). In fuzzy clustering, the FCM algorithm and its variations are well known and the most used in various applications. We know that the robustness is important for clustering (see [6]) However, the robustness for these FCM and various extended fuzzy clustering algorithms still needs for further study. In this talk, we shall focus the robustness for these fuzzy clustering algorithms. We use the o function of M-estimate to analyze the robustness for fuzzy clustering algorithms and then propose their improvements. On the other hand, cluster validity indexes can be used to evaluate the fitness of data partitions produced by a fuzzy clustering algorithm (see [7-9]). However, the values of validity indexes may be heavily influenced by noise and outliers. In the literature, there is little discussion about the robustness of cluster validity indexes. In this talk, we also analyze the robustness of a validity index using the o function of M-estimate. We then improve most fuzzy cluster validity indexes so that they will be more robust for noise and outliers. Some comparative examples with numerical and real data sets will be presented.