Non-flat clustering whith 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 gener- alizes 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 represen- tational Bregman divergences, we show that an α-divergence based k-means algorithm can be designed. We present pre- liminary 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.

• Type: Conference
• Year: 2011
• Where: ICASSP
• Authors: Olivier Schwander, Frank Nielsen
• Keywords: Alpha-divergence, Clustering, Informa- Tion Geometry, K-means