Checking the Sufficiently Scattered Condition using a Global Non-Convex Optimization Software
<|reference_start|>Checking the Sufficiently Scattered Condition using a Global Non-Convex Optimization Software: 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.<|reference_end|>
@article{gillis2024checking,
    title={Checking the Sufficiently Scattered Condition using a Global Non-Convex
  Optimization Software},
    author={Nicolas Gillis, Robert Luce},
    journal={arXiv preprint arXiv:2402.06019},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.06019},
    primaryClass={cs.LG eess.SP math.OC stat.ML}
}