Maximum-distance nonnegative matrix factorization for unmixing highly mixed grain-size distribution data: A generalization of AnalySize
2026-08-24 • Machine Learning
Machine Learning
AI summaryⓘ
The authors studied a way to break down grain-size data, which are nonnegative and sum up to one, into simpler parts using a method called nonnegative matrix factorization (NMF). They found that an existing method called AnalySize works well when the data is not mixed much but struggles when data points are very mixed and unclear. To fix this, the authors created a new approach that tries to make the basic parts as different from each other as possible. Their experiments show this new method works better on highly mixed grain-size data.
Nonnegative Matrix FactorizationGrain-Size DistributionEnd MembersAnalySizeMaximum-Distance NMFHierarchical Alternating Least SquaresData UnmixingMatrix Decomposition
Authors
Qianqian Qi, Zhongming Chen, Peter G. M. van der Heijden
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.