A methodology for constructing fuzzy algorithms for learning vector quantization

This paper presents a general methodology for the development of fuzzy algorithms for learning vector quantization (FALVQ). The design of specific FALVQ algorithms according to existing approaches reduces to the selection of the membership function assigned to the weight vectors of an LVQ competitive neural network, which represent the prototypes. The development of a broad variety of FALVQ algorithms can be accomplished by selecting the form of the interference function that determines the effect of the nonwinning prototypes on the attraction between the winning prototype and the input of the network. The proposed methodology provides the basis for extending the existing FALVQ 1, FALVQ 2, and FALVQ 3 families of algorithms. This paper also introduces two quantitative measures which establish a relationship between the formulation that led to FALVQ algorithms and the competition between the prototypes during the learning process. The proposed algorithms and competition measures are tested and evaluated using the IRIS data set. The significance of the proposed competition measure is illustrated using FALVQ algorithms to perform segmentation of magnetic resonance images of the brain.