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Some steps towards a general principle for dimensionality reduction mappings

Authors: Barbara Hammer, Kerstin Bunte, and Michael Biehl

Published in: Dagstuhl Seminar Proceedings, Volume 10302, Learning paradigms in dynamic environments (2010)

Abstract

In the past years, many dimensionality reduction methods have been established which allow to visualize high dimensional data sets. Recently, also formal evaluation schemes have been proposed for data visualization, which allow a quantitative evaluation along general principles. Most techniques provide a mapping of a priorly given finite set of points only, requiring additional steps for out-of-sample extensions. We propose a general view on dimensionality reduction based on the concept of cost functions, and, based on this general principle, extend dimensionality reduction to explicit mappings of the data manifold. This offers the possibility of simple out-of-sample extensions. Further, it opens a way towards a theory of data visualization taking the perspective of its generalization ability to new data points. We demonstrate the approach based in a simple example.

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Barbara Hammer, Kerstin Bunte, and Michael Biehl. Some steps towards a general principle for dimensionality reduction mappings. In Learning paradigms in dynamic environments. Dagstuhl Seminar Proceedings, Volume 10302, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{hammer_et_al:DagSemProc.10302.5,
  author =	{Hammer, Barbara and Bunte, Kerstin and Biehl, Michael},
  title =	{{Some steps towards a general principle for dimensionality reduction mappings}},
  booktitle =	{Learning paradigms in dynamic environments},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10302},
  editor =	{Barbara Hammer and Pascal Hitzler and Wolfgang Maass and Marc Toussaint},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10302.5},
  URN =		{urn:nbn:de:0030-drops-28034},
  doi =		{10.4230/DagSemProc.10302.5},
  annote =	{Keywords: Visualization, dimensionality reduction}
}

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Some steps towards a general principle for dimensionality reduction mappings

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