Non-flat clustering whith alpha-divergences

Olivier Schwander (1) , Frank Nielsen (1, 2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 Sony CSL - Sony Computer Science Laboratories

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 alpha-divergences. With the framework for representational Bregman divergences, we show that an alpha-divergence based k-means algorithm can be designed. We present preliminary experiments for clustering and image segmentation applications. Since alpha-divergences are the natural divergences for constant curvature spaces, these experiments are expected to give information on the structure of the data.

Mots clés: alpha-divergence; clustering; information geometry; k-means

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Olivier Schwander, Frank Nielsen. Non-flat clustering whith alpha-divergences. ICASSP, May 2011, Prague, Czech Republic. pp.2100 - 2103, ⟨10.1109/ICASSP.2011.5946740⟩. ⟨hal-00708634⟩