Quantization and clustering with Bregman divergences

 This paper deals with the quantization problem of a random variable X taking values in a separable and reexive Banach space, and with the related question of clustering independent random observations distributed as X. To this aim, we use a quantization scheme with a class of distortion measures called Bregman divergences, and provide conditions ensuring the existence of an optimal quantizer and an empirically optimal quantizer. Rates of convergence are also discussed.

• Type: Journal
• Year: 2010
• Where: MA
• Authors: Aurélie Fischer
• Keywords: Communications, Independent Random Observations, MA 2010, Optimal Quantizer, Reexive Banach Space