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Adaptive k-means clustering algorithms have been used in several artificial neural network architectures, such as radial basis function networks or feature-map classifiers, for a competitive partitioning of the input domain. This paper presents an enhancement of the traditional k-means algorithm. It approximates an optimal clustering solution with an efficient adaptive learning rate, which renders it usable even in situations where the statistics of the problem task varies slowly with time. This modification Is based on the optimality criterion for the k-means partition stating that: all the regions in an optimal k-means partition have the same variations if the number of regions in the partition is large and the underlying distribution for generating input patterns is smooth. The goal of equalizing these variations is introduced in the competitive function that assigns each new pattern vector to the “appropriate” region. To evaluate the optimal k-means algorithm, the authors first compare it to other k-means variants on several simple tutorial examples, then the authors evaluate it on a practical application: vector quantization of image data