Thomas M. Martinetz, Stanislav G. Berkovich, and Klaus Schulten.
``Neural gas'' for vector quantization and its application to
time-series prediction.
IEEE Transactions on Neural Networks, 4:558-569, 1993.
MART93BAs a data compression technique, vector quantization requires the minimalization 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.
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