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Learning Vector Quantization: generalization ability and dynamics of competing prototypes

Authors: Aree Witoelar, Michael Biehl, and Barbara Hammer

Published in: Dagstuhl Seminar Proceedings, Volume 7131, Similarity-based Clustering and its Application to Medicine and Biology (2007)

Abstract

Learning Vector Quantization (LVQ) are popular multi-class classification algorithms. Prototypes in an LVQ system represent the typical features of classes in the data. Frequently multiple prototypes are employed for a class to improve the representation of variations within the class and the generalization ability. In this paper, we investigate the dynamics of LVQ in an exact mathematical way, aiming at understanding the influence of the number of prototypes and their assignment to classes. The theory of on-line learning allows a mathematical description of the learning dynamics in model situations. We demonstrate using a system of three prototypes the different behaviors of LVQ systems of multiple prototype and single prototype class representation.

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Aree Witoelar, Michael Biehl, and Barbara Hammer. Learning Vector Quantization: generalization ability and dynamics of competing prototypes. In Similarity-based Clustering and its Application to Medicine and Biology. Dagstuhl Seminar Proceedings, Volume 7131, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{witoelar_et_al:DagSemProc.07131.5,
  author =	{Witoelar, Aree and Biehl, Michael and Hammer, Barbara},
  title =	{{Learning Vector Quantization: generalization ability and dynamics of competing prototypes}},
  booktitle =	{Similarity-based Clustering and its Application to Medicine and Biology},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7131},
  editor =	{Michael Biehl and Barbara Hammer and Michel Verleysen and Thomas Villmann},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07131.5},
  URN =		{urn:nbn:de:0030-drops-11311},
  doi =		{10.4230/DagSemProc.07131.5},
  annote =	{Keywords: Online learning, learning vector quantization}
}

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Learning Vector Quantization: generalization ability and dynamics of competing prototypes

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