The dynamics of Learning Vector Quantization

M. Biehl (a), A. Ghosh (a), Barbara Hammer (b)
(a) Intelligent Systems Group
(b) Univ. Clausthal-Zellerfeld, Germany


Learning schemes such as Competitive Learning and Learning Vector Quantization (LVQ) are based on the representation of data by appropriately chosen prototype vectors. While intuitively clear and widely used in a variety of classification problems, most algorithms of LVQ are heuristically motivated and lack, for instance, the relation to a well-defined cost function. Nevertheless, methods borrowed from Statistical Physics allow for a systematic study of such learning processes. Model situations in which the training is based on high-dimensional, randomized data can be studied analytically. It is possible, for instance, to compute typical learning curves, i.e. the success of learning vs. the number of example data. Besides the analysis and comparison of standard algorithms, the aim of these studies is to devise novel, more efficient training prescriptions. This talk summarizes our recent results concerning several unsupervised and supervised schemes of Vector Quantization and gives an outlook on forthcoming projects. Furthermore, we would greatly appreciate suggestions concerning potential applications of LVQ training.

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