We propose a new method for clustering based on local minimization of the gamma-divergence, which we call spontaneous clustering. The greatest advantage of the proposed method is that it automatically detects the number of clusters that adequately reflect the data structure. In contrast, existing methods, such as K-means, fuzzy c-means, or model-based clustering need to prescribe the number of clusters. We detect all the local minimum points of the gamma-divergence, by which we define the cluster centers. A necessary and sufficient condition for the gamma-divergence to have local minimum points is also derived in a simple setting. Applications to simulated and real data are presented to compare the proposed method with existing ones.

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