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

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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