“Neural-Gas” Network for Vector Quantization and its Application to Time-Series Prediction

As a data compression technique, vector quantization requires the minimization of a cost function - the distortion error - which, in general, has many local minima. In this paper, a neural network algorithm based on a 'soft-max' adaptation rule is presented that exhibits good performance in reaching the optimum, or at least coming close. The soft-max rule employed is an extension of the standard K-means clustering procedure and takes into account a 'neighborhood ranking' of the reference (weight) vectors. It is shown that the dynamics of the reference (weight) vectors during the input-driven adaptation procedure 1) is determined by the gradient of an energy function whose shape can be modulated through a neighborhood determining parameter, and 2) resembles the dynamics of Brownian particles moving in a potential determined by the data point density. The network is employed to represent the attractor of the Mackey-Glass equation and to predict the Mackey-Glass time series, with additional local linear mappings for generating output values. The results obtained for the time-series prediction compare very favorably with the results achieved by back-propagation and radial basis function networks.