提出最大化端元距离的NMF方法，提升高混合粒径数据分解效果。
Maximum-distance nonnegative matrix factorization for unmixing highly mixed grain-size distribution data: A generalization of AnalySize
- 通过最大化端元间距离增强分解稳定性
- 在高度混合数据上实现准确端元识别
- 适合地质、土壤等复杂混合样本分析
非负矩阵分解（NMF）能将非负矩阵分解为两个非负矩阵的乘积，适用于具有非负性和行和为1特性的粒径分布数据。以往研究显示，基于NMF的AnalySize方法在低混合数据中表现良好，但在高度混合数据中失效，因无观测样本接近真实端元。为此，本文提出最大距离NMF，通过最大化估计端元间的差异性来克服此问题，并设计分层交替最小二乘优化算法。该方法可视为AnalySize的推广：AnalySize最小化端元间距离，而本方法则最大化距离。实验表明，该方法能有效分解高度混合的粒径分布数据。
原文摘要 · Abstract (English)
Nonnegative matrix factorization (NMF) decomposes a nonnegative matrix into the product of two nonnegative matrices. This property makes NMF well suited for unmixing grain-size distribution data, which are inherently nonnegative and have row sums equal to one. Previous studies have shown that AnalySize, an NMF-based method, performs well on poorly mixed grain-size distribution data but struggles when the data is highly mixed, where no observed samples are close to the true end members. To overcome this limitation, we introduce a maximum-distance NMF that encourages the estimated end members to be as distinct as possible and develop a hierarchical alternating least squares algorithm for optimization. The proposed formulation can be regarded as a generalization of AnalySize, where AnalySize minimizes the distance among end members while the proposed method maximizes it. Experimental results demonstrate that the method effectively decomposes highly mixed grain-size distribution data.
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