Non-flat clustering with alpha-divergences

The scope of the well-known k-means algorithm has been broadly extended with some recent results: first, the k-means++ initialization method gives some approximation guarantees; second, the Bregman k-means algorithm generalizes the classical algorithm to the large family of Bregman divergences. The Bregman seeding framework combines approximation guarantees with Bregman divergences. We present here an extension of the k-means algorithm using the family of α-divergences. With the framework for representational Bregman divergences, we show that an α-divergence based k-means algorithm can be designed. We present preliminary experiments for clustering and image segmentation applications. Since α-divergences are the natural divergences for constant curvature spaces, these experiments are expected to give information on the structure of the data.