Correcting Jaccard and other similarity indices for chance agreement in cluster analysis
Advances in Data Analysis and Classification
Information Sciences: an International Journal
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This paper proposes a maximum clustering similarity (MCS) method for determining the number of clusters in a data set by studying the behavior of similarity indices comparing two (of several) clustering methods. The similarity between the two clusterings is calculated at the same number of clusters, using the indices of Rand (R), Fowlkes and Mallows (FM), and Kulczynski (K) each corrected for chance agreement. The number of clusters at which the index attains its maximum is a candidate for the optimal number of clusters. The proposed method is applied to simulated bivariate normal data, and further extended for use in circular data. Its performance is compared to the criteria discussed in Tibshirani, Walther, and Hastie (2001). The proposed method is not based on any distributional or data assumption which makes it widely applicable to any type of data that can be clustered using at least two clustering algorithms.