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Given an m-by-n matrix M and a factorization rank r, nonnegative matrix factorization (NMF) looks for an m-by-r nonnegative matrix U and a r-by-n nonnegative matrix V such that M ≈ UV.  

This website gathers the following: 

(1) A data set containing nonnegative matrices for which it is important to compute exact NMF's (see Data Set), and a library of heuristics to compute exact NMF's (see Heuristics). 

See A. Vandaele, N. Gillis, F. Glineur and D. Tuyttens, "Heuristics for Exact Nonnegative Matrix Factorization",  Journal of Global Optimization 65 (2), pp 369-400, 2016.  [doi] [arXiv] [pdf]

(2) A code to compute the exact NMF of the slack matrices of regular n-gons (see Regular n-gons). 

See A. Vandaele, N. Gillis and F. Glineur, "On the Linear Extension Complexity of Regular n-gons", Linear Algebra and its Applications 521, pp. 217–239, 2017. [doi] [arXiv] [pdf]

(3) A code to compute positive semidefinite (PSD) factorizations, which are a generalization of NMF (see PSD Factorization). The code can also be used  to compute completely PSD factorizations. 

See A. Vandaele, F. Glineur and N. Gillis, Algorithms for Positive Semidefinite Factorization, Computational Optimization and Applications 71 (1), pp. 193-219, 2018. [doi] [arXiv] [pdf]