提出新条件，证明最小体积NMF在噪声下仍能准确还原真实因子。
Robustness of Minimum-Volume Nonnegative Matrix Factorization under an Expanded Sufficiently Scattered Condition
- 基于扩展充分散射条件，设计稳健的NMF重构方法。
- 在噪声环境下仍可精确恢复原始基向量与系数矩阵。
- 适合高维数据如光谱分析、主题建模等场景使用。
最小体积非负矩阵分解（min-vol NMF）已成功应用于高光谱成像、化学动力学、光谱学、主题建模和音频源分离等领域。然而，其对噪声的鲁棒性长期是个未解难题。本文证明，在称为扩展充分散射条件的假设下，min-vol NMF能在噪声存在时准确识别出真实因子。该条件要求数据点在由基向量生成的潜在单纯形中足够充分地分散。
原文摘要 · Abstract (English)
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.
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