Abstract
In recent years, a number of methods for solving the constrained non-negative matrix factorization problem have been proposed. In this paper, we propose an efficient method for tackling the ever increasing size of real-world problems. To this end, we propose a general relaxation and several algorithms for enforcing constraints in a challenging application: the phase-mapping problem in materials science. Using experimental data we show that the proposed method significantly outperforms previous methods in terms of \(\ell _2\)-norm error and speed.
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Acknowledgments
Work supported by an NSF Expedition award for Computational Sustainability (CCF-1522054), NSF Computing Research Infrastructure (CNS-1059284), NSF Inspire (1344201), a MURI/AFOSR grant (FA9550), and a grant from the Toyota Research Institute.
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Bai, J., Ament, S., Perez, G., Gregoire, J., Gomes, C. (2018). An Efficient Relaxed Projection Method for Constrained Non-negative Matrix Factorization with Application to the Phase-Mapping Problem in Materials Science. In: van Hoeve, WJ. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2018. Lecture Notes in Computer Science(), vol 10848. Springer, Cham. https://doi.org/10.1007/978-3-319-93031-2_4
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