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.

翻译：充分分散条件（SSC）是研究多种矩阵分解问题可辨识性的关键条件，这些分解问题包括非负矩阵分解、最小体积矩阵分解、对称矩阵分解、单纯形结构矩阵分解以及多面体矩阵分解。SSC能够保证计算得到的矩阵分解在除去平凡歧义后具有唯一性/可辨识性。然而，在一般情况下检验该条件是NP难的。本文证明，在现实场景中，当分解秩不太大时，该条件可以在合理时间内得到检验。这一实现通过将问题表述为有界集合上的非凸二次优化问题达成。我们采用全局非凸优化软件Gurobi，并在合成数据集与真实高光谱图像上展示了该代码的有效性。