Quantization and clustering with Bregman divergences

This paper deals with the problem of quantization of a random variable XX taking values in a separable and reflexive Banach space, and with the related question of clustering independent random observations distributed as XX. To this end, 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.