{"ID":2845304,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.04291","arxiv_id":"2511.04291","title":"Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Condition","abstract":"Minimum-volume nonnegative matrix factorization (min-vol NMF) has been used successfully in many applications, such as hyperspectral imaging, chemical kinetics, spectroscopy, topic modeling, and audio source separation. However, its robustness to noise has been a long-standing open problem. In this paper, we prove that min-vol NMF identifies the groundtruth factors in the presence of noise under a condition referred to as the expanded sufficiently scattered condition which requires the data points to be sufficiently well scattered in the latent simplex generated by the basis vectors.","short_abstract":"Minimum-volume nonnegative matrix factorization (min-vol NMF) has been used successfully in many applications, such as hyperspectral imaging, chemical kinetics, spectroscopy, topic modeling, and audio source separation. However, its robustness to noise has been a long-standing open problem. In this paper, we prove that...","url_abs":"https://arxiv.org/abs/2511.04291","url_pdf":"https://arxiv.org/pdf/2511.04291v1","authors":"[\"Giovanni Barbarino\",\"Nicolas Gillis\",\"Subhayan Saha\"]","published":"2025-11-06T11:36:32Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"eess.SP\",\"math.NA\"]","methods":"[]","has_code":false}