## Greedy vector quantization

 Title Greedy vector quantization Publication Type Journal Article Year of Publication 2014 Authors Harald Luschgy, and Gilles Pagès Journal Preprint Abstract We investigate the greedy version of the -optimal vector quantization problem for an -valued random vector . We show the existence of a sequence such that minimizes (-mean quantization error at level induced by ). We show that this sequence produces -rate optimal -tuples (i.e. the -mean quantization error at level induced by goes to at rate . Greedy optimal sequences also satisfy, under natural additional assumptions, the distortion mismatch property: the -tuples remain rate-optimal with respect to the -norms, . Finally, we propose optimization methods to compute greedy sequences, adapted from usual Lloyd’s I and Competitive Learning Vector Quantization procedures, either in their deterministic (implementable when ) or stochastic versions.