DagSemProc.07071.16.pdf
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The Sinkhorn-Knopp Algorithm:Convergence and Applications
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Dagstuhl Seminar Proceedings, Volume 7071
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2007-06-28
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Philip A. Knight. The Sinkhorn-Knopp Algorithm:Convergence and Applications. In Web Information Retrieval and Linear Algebra Algorithms. Dagstuhl Seminar Proceedings, Volume 7071, pp. 1-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)
https://doi.org/10.4230/DagSemProc.07071.16
https://doi.org/10.4230/DagSemProc.07071.16
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.
Keywords
- Matrix balancing
- Sinkhorn-Knopp algorithm
- PageRank
- doubly stochastic matrix
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