使用全局非凸优化软件检验充分分散条件
Checking the Sufficiently Scattered Condition using a Global Non-Convex Optimization Software
AI总结：
本文将充分分散条件检验转化为有界集合上的非凸二次优化问题，利用 Gurobi 在分解秩适中时实现合理时间内的全局检验，并通过合成数据与高光谱图像验证其实用性。
摘要：
充分分散条件（SSC）是研究各类矩阵分解问题可辨识性的关键条件，这些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和多面体矩阵分解。SSC 能够保证所计算出的矩阵分解在除去平凡歧义后是唯一的/可辨识的。然而，一般而言检验该条件是 NP 难的。本文表明，在现实场景中，当分解秩不太大时，仍可在合理时间内完成检验。实现方式是将该问题表述为有界集合上的非凸二次优化问题。我们使用全局非凸优化软件 Gurobi，并在合成数据集和真实高光谱图像上展示了该代码的实用性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
