FUZZY ALGORITHMS FOR LEARNING VECTOR QUANTIZATION

This paper presents the development of fuzzy algorithms for learning v ector quantization (FALVQ). These algorithms are derived by minimizing the weighted sum of the squared Euclidean distances between an input vector, which represents a feature vector, and the weight vectors of a competitive learning vector quantization (LVQ) network, which represe nt the prototypes. This formulation Leads to competitive algorithms, w hich allow each input vector to attract all prototypes. The strength o f attraction between each input and the prototypes is determined by a set of membership functions, which can be selected on the basis of spe cific criteria, A gradient-descent-based learning rule is derived for a general class of admissible membership functions which satisfy certa in properties. The FALVQ 1, FALVQ 2, and FALVQ 3 families of algorithm s are developed by selecting admissible membership functions with diff erent properties, The proposed algorithms are tested and evaluated usi ng the IRIS data set, The efficiency of the proposed algorithms is als o illustrated by their use in codebook design required for image compr ession based on vector quantization.