Some new competitive learning schemes
James C. Bezdek, Nikhil Ranjan Pal, Richard J. Hathaway, Nicolaos B. Karayiannis · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
First, we identify an algorithmic defect of the generalized learning vector quantization (GLVQ) scheme that causes it to behave erratically for a certain scaling of the input data. We demonstrate the problem using the IRIS data. Then, we show that GLVQ can behave incorrectly because its learning rates are reciprocally dependent on the sum of squares of distances from an input vector to the node weight vectors. Finally, we propose a new family of models -- the GLVQ-F family -- that remedies the problem. We derive algorithms for competitive learning using the GLVQ-F model, and prove that they are invariant to all positive scalings of the data. The learning rule for GLVQ-F updates all nodes using a learning rate function which is inversely proportional to their distance from the input data point. We illustrate the failure of GLVQ and success of GLVQ-F with the ubiquitous IRIS data.