Robust cluster validity indexes

Cluster validity indexes can be used to evaluate the fitness of data partitions produced by a clustering algorithm. Validity indexes are usually independent of clustering algorithms. However, the values of validity indexes may be heavily influenced by noise and outliers. These noise and outliers may not influence the results from clustering algorithms, but they may affect the values of validity indexes. In the literature, there is little discussion about the robustness of cluster validity indexes. In this paper, we analyze the robustness of a validity index using the ϕϕ function of M-estimate and then propose several robust-type validity indexes. Firstly, we discuss the validity measure on a single data point and focus on those validity indexes that can be categorized as the mean type of validity indexes. We then propose median-type validity indexes that are robust to noise and outliers. Comparative examples with numerical and real data sets show that the proposed median-type validity indexes work better than the mean-type validity indexes.