Two soft relatives of learning vector quantization

Abstract

Learning vector quantization 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=FLVQ. These algorithms both extend the update neighborhood to all nodes in the network. SCS is a sequential, deterministic method with learning rates that are partially based on posterior probabilities. FLVQ is a batch algorithm whose learning rates are derived from fuzzy memberships. We show that SCS learning rates can be interpreted in terms of statistical decision theory, and derive several relationships between SCS and FLVQ. Limit analysis shows that the learning rates of these two algorithms have opposite tendencies. Numerical examples illustrate the difficulty of choosing good algorithmic parameters for SCS. Finally, we elaborate the relationship between FL VQ, Fuzzy c-Means, Hard c-Means, a batch version of LVQ and SCS.