发表机构
Hangzhou Dianzi University; Utrecht University; University of Southampton（杭州电子科技大学; 乌得勒支大学; 南安普顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对高度混合粒度分布数据的解混问题，提出了 AnalySize 的推广方法——最大距离非负矩阵分解，通过最大化端元间距离结合分层交替最小二乘算法，实现了对高度混合数据的有效分解。
AI 中文摘要
非负矩阵分解（NMF）将一个非负矩阵分解为两个非负矩阵的乘积，该特性使 NMF 非常适合解混粒度分布数据，这类数据本质上是非负的，且行和为 1。过往研究表明，基于 NMF 的方法 AnalySize 在混合程度低的粒度分布数据上表现良好，但在数据高度混合时会遇到困难——此时没有观测样本接近真实端元。为克服这一局限，我们引入最大距离非负矩阵分解，鼓励估计的端元尽可能不同，并开发了一种用于优化的分层交替最小二乘算法。所提出的公式可视为 AnalySize 的推广：AnalySize 最小化端元间的距离，而本文方法则最大化该距离。实验结果表明，该方法能有效分解高度混合的粒度分布数据。
英文摘要
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.
