Neural networks for Vector Quantization (VQ) such as K-means, Neural-Gas (NG) network and Kohonen's Self-Organizing Map (SOM) have been proposed. K-means, which is a "hard-max" approach, converges very fast. The method, however, devotes itself to local search, and it easily falls into local minima. On the other hand, the NG and SOM methods, which are "soft-max" approaches, are good at the global search ability. Though NG and SOM exhibit better performance in coming close to the optimum than that of K-means, the methods converge slower than K-means. In order to the disadvantages that exist when K-means, NG and SOM are used individually, this paper proposes hybrid methods such as NG-K, SOM-K and SOM-NG. NG-K performs NG adaptation during short period of time early in the learning process, and then the method performs K-means adaptation in the rest of the process. SOM-K and SOM-NG are similar as NG-K. From numerical simulations including an image compression problem, NG-K and SOM-K exhibit better performance than other methods.

In order to construct fuzzy systems automatically, there are many studies on combining fuzzy inference with neural networks. In these studies, fuzzy models using self-organization and vector quantization have been proposed. It is well known that these models construct fuzzy inference rules effectively representing distribution of input data, and not affected by increment of input dimensions. In this paper, we propose a destructive fuzzy modeling using neural gas network and demonstrate the validity of a proposed method by performing some numerical examples.