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Perspectives on CUR decompositions
Institution:1. Department of Mathematics, University of Arizona, Tucson, AZ 85719 USA;2. Department of Mathematics, University of California, Los Angeles, CA 90095, USA;1. IbnTofail University, Kenitra 14000, Morocco;2. National School of Applied Sciences (ENSAK), IbnTofail University, Kenitra 14000, Morocco;1. Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States;2. Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, United States;1. Universität Rostock, Institut für Mathematik, Ulmenstraße 69, 18057, Rostock, Germany;2. Faculty of Chemistry, Institute for Advanced Studies in Basic Sciences, 45195-1159, Zanjan, Iran;3. Leibniz-Institut für Katalyse, Albert-Einstein-Straße 29a, 18059, Rostock, Germany;4. Evonik Performance Materials GmbH, Paul-Baumann Straße 1, 45772, Marl, Germany;5. Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780, Bochum, Germany;1. School of Mathematics and Physics, The University of Queensland, Brisbane, 4072, Australia;2. Center for Data Science, Zhejiang University, 310027, Hangzhou, China;3. School of Data Science and Department of Mathematics, City University of Hong Kong, Hong Kong
Abstract:This note discusses an interesting matrix factorization called the CUR Decomposition. We illustrate various viewpoints of this method by comparing and contrasting them in different situations. Additionally, we offer a new characterization of CUR decompositions which synergizes these viewpoints and shows that they are indeed the same in the exact decomposition case.
Keywords:CUR Decomposition  Low Rank Matrix Approximation  Column Subset Selection
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