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URN: urn:nbn:de:0030-drops-10644
URL: http://drops.dagstuhl.de/opus/volltexte/2007/1064/
Knight, Philip A.

The Sinkhorn-Knopp Algorithm:Convergence and Applications

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Abstract

As long as a square nonnegative matrix $A$ contains sufficient nonzero elements, the Sinkhorn-Knopp algorithm can be used to balance the matrix, that is, to find a diagonal scaling of $A$ that is doubly stochastic. We relate balancing to problems in traffic flow and describe how balancing algorithms can be used to give a two sided measure of nodes in a graph. We show that with an appropriate modification, the Sinkhorn-Knopp algorithm is a natural candidate for computing the measure on enormous data sets.

BibTeX - Entry

@InProceedings{knight:DSP:2007:1064,
  author =	{Philip A. Knight},
  title =	{The Sinkhorn-Knopp Algorithm:Convergence and Applications},
  booktitle =	{Web Information Retrieval and Linear Algebra Algorithms},
  year =	{2007},
  editor =	{Andreas Frommer and Michael W. Mahoney and Daniel B. Szyld},
  number =	{07071},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2007/1064},
  annote =	{Keywords: Matrix balancing, Sinkhorn-Knopp algorithm, PageRank, doubly stochastic matrix}
}

Keywords: Matrix balancing, Sinkhorn-Knopp algorithm, PageRank, doubly stochastic matrix
Seminar: 07071 - Web Information Retrieval and Linear Algebra Algorithms
Issue date: 2007
Date of publication: 28.06.2007

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