Berlin 2005 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 34: Poster

DY 34.21: Poster

Montag, 7. März 2005, 15:30–18:00, Poster TU D

Supervised and unsupervised vector quantization: a solvable model — •Michael Biehl and Anarta Ghosh — Institute of Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands

Unsupervised Vector Quantization (VQ) and supervised (Learning) Vector Quantization (LVQ) are intuitively clear and widely used methods for the analysis of large amounts of structured data. In the former, the aim is the representation of data by a limited number of prototype vectors. In the latter, prototypes serve as reference vectors for a classification based on appropriate distance measures. We apply statistical physics methods in order to study analytically the dynamics and stability of various learning algorithms in a model situation. In particular, we compare unsupervised competitive learning with Kohonen’s original formulation of LVQ and several modifications thereof. Recent attempts to identify appropriate cost functions for LVQ are also taken into account. We show that many appearently plausible approaches suffer from instability problem, in particular when the data belongs predominantly to one of the classes. The development of simple prescriptions which approximate (Bayes) optimal classification schemes under rather general circumstances is in the center of our interest.