License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/DagSemProc.07071.16
URN: urn:nbn:de:0030-drops-10644
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Knight, Philip A.

The Sinkhorn-Knopp Algorithm:Convergence and Applications

07071.KnightPhilip.Paper.1064.pdf (0.5 MB)


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

  author =	{Knight, Philip A.},
  title =	{{The Sinkhorn-Knopp Algorithm:Convergence and Applications}},
  booktitle =	{Web Information Retrieval and Linear Algebra Algorithms},
  pages =	{1--18},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7071},
  editor =	{Andreas Frommer and Michael W. Mahoney and Daniel B. Szyld},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-10644},
  doi =		{10.4230/DagSemProc.07071.16},
  annote =	{Keywords: Matrix balancing, Sinkhorn-Knopp algorithm, PageRank, doubly stochastic matrix}

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

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