Stationarity of Matrix Relevance Learning Vector Quantization
Michael L. Biehl, Barbara Hammer, Frank-Michael Schleif, Petra Schneider, Thomas Villmann · PUB – Publications at Bielefeld University (Bielefeld University) · 2009
We investigate the convergence properties of heuristic matrix relevance updates in Learning Vector Quantization. Under mild assumptions on the training process, stationarity conditions can be worked out which characterize the outcome of training in terms of the relevance matrix. It is shown that the original training schemes single out one specific direction in feature space which depends on the statistical properties of the data relative to the approached prototype configuration. Appropriate regularization terms can be used to favor full rank relevance matrices and to prevent oversimplification effects. The structure of the stationary solution is derived, giving insight into the influence of the regularization parameter. Machine Learning Reports,Research group on Computational Intelligence, http://www.uni-leipzig.de/compint Stationarity of Matrix Relevance Learning Vector Quantization