License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/DagSemProc.10302.5
URN: urn:nbn:de:0030-drops-28034
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Hammer, Barbara ; Bunte, Kerstin ; Biehl, Michael

Some steps towards a general principle for dimensionality reduction mappings

10302.HammerBarbara.Paper.2803.pdf (0.2 MB)


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

BibTeX - Entry

  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 =		{},
  URN =		{urn:nbn:de:0030-drops-28034},
  doi =		{10.4230/DagSemProc.10302.5},
  annote =	{Keywords: Visualization, dimensionality reduction}

Keywords: Visualization, dimensionality reduction
Collection: 10302 - Learning paradigms in dynamic environments
Issue Date: 2010
Date of publication: 05.11.2010

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