Lower bound computations for the nonnegative rank

Samuel Fiorini; Krystal Guo; Marco Macchia; Matthias Walter

Lower bound computations for the nonnegative rank

Samuel Fiorini, Krystal Guo, Marco Macchia, Matthias Walter

University of Twente

Research output: Contribution to conference › Paper › Academic › peer-review

Abstract

The nonnegative rank of a matrix is the smallest inner dimension when writing it as a product of two nonnegative matrices. Such nonnegative matrix factorizations have numerous applications in machine learning and data mining, where one usually allows inexact factorizations. The exact counterpart is related to the so-called extension complexity of a polytope, an important parameter in combinatorial optimization. We implemented different algorithms for computing lower bounds on the nonnegative rank of a matrix. In this extended abstract we focus on results that relate our best algorithms' performance to the size of the matrix.

Original language	English
Pages	41-44
Number of pages	4
Publication status	Published - 1 Jan 2019
Event	17th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2019 - U-Parkhotel, Enschede, Netherlands Duration: 1 Jul 2019 → 3 Jul 2019 Conference number: 17 http://wwwhome.math.utwente.nl/~ctw/

Workshop

Workshop	17th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2019
Abbreviated title	CTW 2019
Country	Netherlands
City	Enschede
Period	1/07/19 → 3/07/19
Internet address	http://wwwhome.math.utwente.nl/~ctw/

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title = "Lower bound computations for the nonnegative rank",

abstract = "The nonnegative rank of a matrix is the smallest inner dimension when writing it as a product of two nonnegative matrices. Such nonnegative matrix factorizations have numerous applications in machine learning and data mining, where one usually allows inexact factorizations. The exact counterpart is related to the so-called extension complexity of a polytope, an important parameter in combinatorial optimization. We implemented different algorithms for computing lower bounds on the nonnegative rank of a matrix. In this extended abstract we focus on results that relate our best algorithms' performance to the size of the matrix.",

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N2 - The nonnegative rank of a matrix is the smallest inner dimension when writing it as a product of two nonnegative matrices. Such nonnegative matrix factorizations have numerous applications in machine learning and data mining, where one usually allows inexact factorizations. The exact counterpart is related to the so-called extension complexity of a polytope, an important parameter in combinatorial optimization. We implemented different algorithms for computing lower bounds on the nonnegative rank of a matrix. In this extended abstract we focus on results that relate our best algorithms' performance to the size of the matrix.

AB - The nonnegative rank of a matrix is the smallest inner dimension when writing it as a product of two nonnegative matrices. Such nonnegative matrix factorizations have numerous applications in machine learning and data mining, where one usually allows inexact factorizations. The exact counterpart is related to the so-called extension complexity of a polytope, an important parameter in combinatorial optimization. We implemented different algorithms for computing lower bounds on the nonnegative rank of a matrix. In this extended abstract we focus on results that relate our best algorithms' performance to the size of the matrix.

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