What you will gain by rounding : theory and algorithms for rounding rank

Neumann, Stefan ; Gemulla, Rainer ; Miettinen, Pauli

What You Will Gain By Rounding Theory and Algorithms for Rounding Rank.pdf - Published

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DOI: https://doi.org/10.1109/ICDM.2016.0049
URL: https://madoc.bib.uni-mannheim.de/42465
Additional URL: http://dws.informatik.uni-mannheim.de/fileadmin/le...
URN: urn:nbn:de:bsz:180-madoc-424650
Document Type: Conference or workshop publication
Year of publication: 2016
Book title: 16th IEEE International Conference on Data Mining : 12-15 December 2016, Barcelona, Catalonia, Spain : proceedings
Page range: 380-389
Conference title: 16th International Conference on Data Mining (ICDM)
Location of the conference venue: Barcelona, Spain
Date of the conference: 12-15 Dec. 2016
Publisher: Bonchi, Francesco
Place of publication: Piscataway, NJ
Publishing house: IEEE
ISBN: 978-1-5090-5474-9 , 978-1-5090-5472-5 , 978-1-5090-5473-2
ISSN: 2374-8486
Publication language: English
Institution: School of Business Informatics and Mathematics > Practical Computer Science I: Data Analytics (Gemulla 2014-)
Subject: 004 Computer science, internet
Abstract: When factorizing binary matrices, we often have to make a choice between using expensive combinatorial methods that retain the discrete nature of the data and using continuous methods that can be more efficient but destroy the discrete structure. Alternatively, we can first compute a continuous factorization and subsequently apply a rounding procedure to obtain a discrete representation. But what will we gain by rounding? Will this yield lower reconstruction errors? Is it easy to find a low-rank matrix that rounds to a given binary matrix? Does it matter which threshold we use for rounding? Does it matter if we allow for only non-negative factorizations? In this paper, we approach these and further questions by presenting and studying the concept of rounding rank. We show that rounding rank is related to linear classification, dimensionality reduction, and nested matrices. We also report on an extensive experimental study that compares different algorithms for finding good factorizations under the rounding rank model.

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