mlsanityData to 7 Oct 2026

Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Condition

arXiv 2511.04291 ↗First posted 6 Nov 2025stat.ML cs.LG cs.NAcited by 0

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 25 of its 62 references that are in the map. First posted on arXiv 6 Nov 2025.

Builds on

25 of 62 references.

References · 25

  1. 2021Provably End-to-end Label-Noise Learning without Anchor Pointscited by 97
  2. 2014Generalized Low Rank Modelscited by 55
  3. 2018Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applicationscited by 55
  4. 2017On Identifiability of Nonnegative Matrix Factorizationcited by 34
  5. 2016Robust Volume Minimization-Based Matrix Factorization for Remote Sensing and Document Clusteringcited by 28
  6. 2014Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Casecited by 26
  7. 2019Crowdsourcing via Pairwise Co-occurrences: Identifiability and Algorithmscited by 23
  8. 2020Simplex-Structured Matrix Factorization: Sparsity-based Identifiability and Provably Correct Algorithmscited by 21
  9. 2017Maximum Volume Inscribed Ellipsoid: A New Simplex-Structured Matrix Factorization Framework via Facet Enumeration and Convex Optimizationcited by 18
  10. 2019Blind Audio Source Separation with Minimum-Volume Beta-Divergence NMFcited by 16
  11. 2013Semidefinite Programming Based Preconditioning for More Robust Near-Separable Nonnegative Matrix Factorizationcited by 13
  12. 2021Learning a Latent Simplex in Input-Sparsity Timecited by 11
13 more
  1. 2020Recovering Joint Probability of Discrete Random Variables from Pairwise Marginalscited by 10
  2. 2014Exact and Heuristic Algorithms for Semi-Nonnegative Matrix Factorizationcited by 9
  3. 2021Probabilistic Simplex Component Analysiscited by 8
  4. 2013Ellipsoidal Rounding for Nonnegative Matrix Factorization Under Noisy Separabilitycited by 7
  5. 2018On Statistical Learning of Simplices: Unmixing Problem Revisitedcited by 5
  6. 2023Deep Clustering with Incomplete Noisy Pairwise Annotations: A Geometric Regularization Approachcited by 5
  7. 2024Checking the Sufficiently Scattered Condition using a Global Non-Convex Optimization Softwarecited by 3
  8. 2024On the Robustness of the Successive Projection Algorithmcited by 3
  9. 2013Fixed points of the EM algorithm and nonnegative rank boundariescited by 2
  10. 2015Robustness Analysis of Preconditioned Successive Projection Algorithm for General Form of Separable NMF Problemcited by 2
  11. 2019Minimum Volume Topic Modelingcited by 2
  12. 2025Fundamental Limits of Learning High-dimensional Simplices in Noisy Regimescited by 2
  13. 2025Identifiability of Nonnegative Tucker Decompositions -- Part I: Theorycited by 1

Built on by

Not cited yet.