Maximum-distance nonnegative matrix factorization for unmixing highly mixed grain-size distribution data: A generalization of AnalySize

2026-08-23

AI Summary

该研究提出了一种最大距离非负矩阵分解方法，用于解决高度混合的粒径分布数据分解问题，通过最大化末端成员间的距离，并使用层次交替最小二乘法进行优化。

Abstract

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.

Problem

• nonnegative matrix factorization
• grain-size distribution data
• highly mixed

Innovation

• maximum-distance NMF
• hierarchical alternating least squares algorithm
• highly mixed grain-size distribution data