Contamination of scattered observations, which are either featureless or unlike the other observations, frequently degrades the performance of standard methods such as K -means and model-based clustering. In this letter, we propose a robust clustering method in the presence of scattered observations called Gamma-clust. Gamma-clust is based on a robust estimation for cluster centers using gamma-divergence. It provides a proper solution for clustering in which the distributions for clustered data are nonnormal, such as t -distributions with different variance-covariance matrices and degrees of freedom. As demonstrated in a simulation study and data analysis, Gamma-clust is more flexible and provides superior results compared to the robustified K -means and model-based clustering.

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.