mlsanityData to 7 Oct 2026

Checking the Sufficiently Scattered Condition using a Global Non-Convex Optimization Software

arXiv 2402.06019 ↗First posted 8 Feb 2024cs.LG eess.SP math.OCcited by 3

Not on the map. Why?

Abstract (arXiv)

The sufficiently scattered condition (SSC) is a key condition in the study of identifiability of various matrix factorization problems, including nonnegative, minimum-volume, symmetric, simplex-structured, and polytopic matrix factorizations. The SSC allows one to guarantee that the computed matrix factorization is unique/identifiable, up to trivial ambiguities. However, this condition is NP-hard to check in general. In this paper, we show that it can however be checked in a reasonable amount of time in realistic scenarios, when the factorization rank is not too large. This is achieved by formulating the problem as a non-convex quadratic optimization problem over a bounded set. We use the global non-convex optimization software Gurobi, and showcase the usefulness of this code on synthetic data sets and on real-world hyperspectral images.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 17 of its 34 references that are in the map. First posted on arXiv 8 Feb 2024.

Builds on

17 of 34 references.

References · 17

  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. 2017Hyperspectral Unmixing: Ground Truth Labeling, Datasets, Benchmark Performances and Surveycited by 33
  6. 2016Robust Volume Minimization-Based Matrix Factorization for Remote Sensing and Document Clusteringcited by 28
  7. 2014Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Casecited by 26
  8. 2019Crowdsourcing via Pairwise Co-occurrences: Identifiability and Algorithmscited by 23
  9. 2020Simplex-Structured Matrix Factorization: Sparsity-based Identifiability and Provably Correct Algorithmscited by 21
  10. 2017Maximum Volume Inscribed Ellipsoid: A New Simplex-Structured Matrix Factorization Framework via Facet Enumeration and Convex Optimizationcited by 18
  11. 2019Blind Audio Source Separation with Minimum-Volume Beta-Divergence NMFcited by 16
  12. 2016Anchor-Free Correlated Topic Modeling: Identifiability and Algorithmcited by 15
5 more
  1. 2022Polytopic Matrix Factorization: Determinant Maximization Based Criterion and Identifiabilitycited by 14
  2. 2019Algorithms and Comparisons of Non-negative Matrix Factorization with Volume Regularization for Hyperspectral Unmixingcited by 10
  3. 2020Recovering Joint Probability of Discrete Random Variables from Pairwise Marginalscited by 10
  4. 2022Bounded Simplex-Structured Matrix Factorization: Algorithms, Identifiability and Applicationscited by 5
  5. 2023Deep Clustering with Incomplete Noisy Pairwise Annotations: A Geometric Regularization Approachcited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 1.

3 papers.

  1. 2025Identifiability of Nonnegative Tucker Decompositions -- Part I: Theorycited by 1
  2. 2026Maximum-Volume Nonnegative Matrix Factorizationcited by 1
  3. 2025Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Conditioncited by 0