Exact Nonnegative Matrix Factorization via Cone-Ray Witnesses: Obtuseness Ranking, Saturation Curves, and an Augmented Alt-LP Breakthrough (opens in new tab)

We study exact nonnegative matrix factorization (NMF) of small exact-rank-r matrices via a cone-ray pipeline combining the truncated SVD, the polyhedral cone of nonnegative preimages, the Double Description Method (DDM, via Fukuda's cddlib), and an alternating linear program (alt-LP) for slack minimisation. Under a uniform-support restriction the factorisation constraint Q P^T = I_r reduces to entrywise nonnegativity of an r x r witness matrix...