An Efficient Relaxed Projection Method for Constrained Non-negative Matrix Factorization with Application to the Phase-Mapping Problem in Materials Science

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10848)


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.



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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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceCornell UniversityIthacaUSA
  2. 2.Joint Center for Artificial PhotosynthesisCalifornia Institute of TechnologyPasadenaUSA

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