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Relaxation Methods for Constrained Matrix Factorization Problems: Solving the Phase Mapping Problem in Materials Discovery

Bai, Junwen and Bjorck, Johan and Xue, Yexiang and Suram, Santosh K. and Gregoire, John and Gomes, Carla (2017) Relaxation Methods for Constrained Matrix Factorization Problems: Solving the Phase Mapping Problem in Materials Discovery. In: Integration of AI and OR Techniques in Constraint Programming. Lecture Notes in Computer Science . No.10335. Springer , Cham, Switzerland, pp. 104-112. ISBN 978-3-319-59775-1.

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Matrix factorization is a robust and widely adopted technique in data science, in which a given matrix is decomposed as the product of low rank matrices. We study a challenging constrained matrix factorization problem in materials discovery, the so-called phase mapping problem. We introduce a novel “lazy” Iterative Agile Factor Decomposition (IAFD) approach that relaxes and postpones non-convex constraint sets (the lazy constraints), iteratively enforcing them when violations are detected. IAFD interleaves multiplicative gradient-based updates with efficient modular algorithms that detect and repair constraint violations, while still ensuring fast run times. Experimental results show that IAFD is several orders of magnitude faster and its solutions are also in general considerably better than previous approaches. IAFD solves a key problem in materials discovery while also paving the way towards tackling constrained matrix factorization problems in general, with broader implications for data science.

Item Type:Book Section
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Suram, Santosh K.0000-0001-8170-2685
Gregoire, John0000-0002-2863-5265
Additional Information:© 2017 Springer International Publishing AG. First Online: 31 May 2017.
Subject Keywords:Constrained matrix factorization; Relaxation methods; Multiplicative updates; Phase-mapping
Series Name:Lecture Notes in Computer Science
Issue or Number:10335
Record Number:CaltechAUTHORS:20170711-130810289
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78951
Deposited By: Tony Diaz
Deposited On:11 Jul 2017 21:07
Last Modified:15 Nov 2021 17:44

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