Weighted fuzzy learning vector quantization and weighted fuzzy c-means algorithms

This paper derives a broad variety of weighted fuzzy learning vector quantization algorithms. These algorithms map a set of feature vectors into a set of prototypes by adapting the weight vectors associated with a competitive neural network through an unsupervised learning process. The derivation of the proposed algorithms is accomplished by minimizing the average weighted generalized mean between the feature vectors and the prototypes using gradient descent. The existing fuzzy learning vector quantization algorithms are interpreted as a special case of the proposed algorithms. Weighted fuzzy c-means algorithms result as a special case of the proposed algorithms if the learning rate is selected at each iteration to satisfy a certain condition.