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A constrained singular value decomposition method that integrates sparsity and orthogonality
Bioinformatics and Biostatistics Hub, Institut Pasteur, Paris, France.ORCID iD: 0000-0002-7421-0655
The Rotman Research Institute, Institution at Baycrest, Toronto, Canada.ORCID iD: 0000-0001-6118-4366
L2S, UMR CNRS 8506, CNRS–Centrale Supélec–Université Paris-Sud, Université Paris-Saclay, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette, France.
Umeå University, Faculty of Medicine, Department of Radiation Sciences, Radiation Physics.ORCID iD: 0000-0001-7119-7646
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2019 (English)In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 14, no 3, article id e0211463Article in journal (Refereed) Published
Abstract [en]

We propose a new sparsification method for the singular value decomposition—called the constrained singular value decomposition (CSVD)—that can incorporate multiple constraints such as sparsification and orthogonality for the left and right singular vectors. The CSVD can combine different constraints because it implements each constraint as a projection onto a convex set, and because it integrates these constraints as projections onto the intersection of multiple convex sets. We show that, with appropriate sparsification constants, the algorithm is guaranteed to converge to a stable point. We also propose and analyze the convergence of an efficient algorithm for the specific case of the projection onto the balls defined by the norms L1 and L2. We illustrate the CSVD and compare it to the standard singular value decomposition and to a non-orthogonal related sparsification method with: 1) a simulated example, 2) a small set of face images (corresponding to a configuration with a number of variables much larger than the number of observations), and 3) a psychometric application with a large number of observations and a small number of variables. The companion R-package, csvd, that implements the algorithms described in this paper, along with reproducible examples, are available for download from https://github.com/vguillemot/csvd.

Place, publisher, year, edition, pages
2019. Vol. 14, no 3, article id e0211463
National Category
Computer Vision and Robotics (Autonomous Systems) Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-157498DOI: 10.1371/journal.pone.0211463ISI: 000461048900010PubMedID: 30865639Scopus ID: 2-s2.0-85062854732OAI: oai:DiVA.org:umu-157498DiVA, id: diva2:1298651
Available from: 2019-03-25 Created: 2019-03-25 Last updated: 2019-04-04Bibliographically approved

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Löfstedt, Tommy

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