Ordered weighted learning vector quantization and clustering algorithms

This paper derives a broad variety of ordered weighted learning vector quantization (LVQ) algorithms. These algorithms map a set of feature vectors in-to a finite set of prototypes by adapting the weight vectors of a competitive neural network through an unsupervised learning process. The derivation of the proposed algorithms is accomplished by minimizing the average ordered weighted generalized mean of the Euclidean distances between the feature vectors and the prototypes using gradient descent. Under certain conditions, the proposed formulation results in ordered weighted clustering algorithms that can also be derived using alternating optimization. Moreover, existing LVQ and clustering algorithms are interpreted as special cases of the proposed formulation.