Journal
INTEGRATION OF AI AND OR TECHNIQUES IN CONSTRAINT PROGRAMMING, CPAIOR 2017
Volume 10335, Issue -, Pages 104-112Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/978-3-319-59776-8_9
Keywords
Constrained matrix factorization; Relaxation methods; Multiplicative updates; Phase-mapping
Funding
- NSF [CCF-1522054, CNS-0832782, CNS-1059284, IIS-1344201, W911-NF-14-1-0498]
- Office of Science of the U.S. Department of Energy [DE-SC0004993]
- U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences [DE-AC02-76SF00515]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [1522054] Funding Source: National Science Foundation
- Div Of Information & Intelligent Systems
- Direct For Computer & Info Scie & Enginr [1344201] Funding Source: National Science Foundation
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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.
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