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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.2

Computing Approximate PSD Factorizations

Authors: Amitabh Basu, Michael Dinitz, and Xin Li

Published in: LIPIcs, Volume 60, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)

Abstract

We give an algorithm for computing approximate PSD factorizations of nonnegative matrices. The running time of the algorithm is polynomial in the dimensions of the input matrix, but exponential in the PSD rank and the approximation error. The main ingredient is an exact factorization algorithm when the rows and columns of the factors are constrained to lie in a general polyhedron. This strictly generalizes nonnegative matrix factorizations which can be captured by letting this polyhedron to be the nonnegative orthant.

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Amitabh Basu, Michael Dinitz, and Xin Li. Computing Approximate PSD Factorizations. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 60, pp. 2:1-2:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{basu_et_al:LIPIcs.APPROX-RANDOM.2016.2,
  author =	{Basu, Amitabh and Dinitz, Michael and Li, Xin},
  title =	{{Computing Approximate PSD Factorizations}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{2:1--2:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Jansen, Klaus and Mathieu, Claire and Rolim, Jos\'{e} D. P. and Umans, Chris},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2016.2},
  URN =		{urn:nbn:de:0030-drops-66258},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.2},
  annote =	{Keywords: PSD rank, PSD factorizations}
}

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Computing Approximate PSD Factorizations

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