Maximum likelihood competitive learning

One popular class of unsupervised algorithms are competitive algo-rithms. In the traditional view of competition, only one competitor, the winner, adapts for any given case. I propose to view compet-itive adaptation as attempting to fit a blend of simple probability generators (such as gaussians) to a set of data-points. The maxi-mum likelihood fit of a model of this type suggests a "softer " form of competition, in which all competitors adapt in proportion to the relative probability that the input came from each competitor. I investigate one application of the soft competitive model, place-ment of radial basis function centers for function interpolation, and show that the soft model can give better performance with little additional computational cost.