<title>Soft learning vector quantization</title>

Abstract

Learning vector quantization (LVQ) often requires extensive experimentation with the learning rate distribution and update neighborhood used during iteration towards good prototypes. A single winner prototype controls the updates. This paper discusses two soft relatives of LVQ: the soft competition scheme (SCS) of Yair et al. and fuzzy LVQ equals FLVQ. These algorithms both extend the update rates that are partially based on posterior probabilities. FLVQ is a batch algorithm whose learning rates are derived from fuzzy memberships. We show several relationships between SCS and FLVQ; and we show that SCS learning rates can be interpreted in terms of statistical decision theory. Finally, we show the relationship between FLVQ, fuzzy c-means, hard c-means, a batch version of LVQ, and SCS.