2 SOFT RELATIVES OF LEARNING VECTOR QUANTIZATION

Learning vector quantization often requires extensive experimentation with the learning rate distribution and update neighborhood used durin g iteration towards good prototypes. A single winner prototype control s the updates. This paper discusses two soft relatives of LVQ: the sof t competition scheme (SCS) of Yair et al. and fuzzy LVQ=FLVQ. These al gorithms both extend the update neighborhood to all nodes in the netwo rk. SCS is a sequential, deterministic method with learning rates that are partially based on posterior probabilities. FLVQ is a batch algor ithm whose learning rates are derived from fuzzy memberships. We show that SCS learning rates can be interpreted in terms of statistical dec ision theory, and derive several relationships between SCS and FLVQ. L imit analysis shows that the learning rates of these two algorithms ha ve opposite tendencies. Numerical examples illustrate the difficulty o f choosing good algorithmic parameters for SCS. Finally, we elaborate the relationship between FLVQ. Fuzzy c-Means, Hard c-Means, a batch ve rsion of LVQ and SCS.