两阶段非负矩阵分解算法及其在光谱解混中的应用  

Two-stage Nonnegative Matrix Factorization Algorithm and Its Application in Hyperspectral Unmixing

作　　者：杨颂 张新元 刘晓[1] 孙莉[1] YANG Song;ZHANG Xin-yuan;LIU Xiao;SUN Li(College of Information Science and Engineering/Shandong Agricultural University,Tai'an 271018,China)

机构地区：[1]山东农业大学信息科学与工程学院,山东泰安271018

出　　处：《山东农业大学学报（自然科学版）》2024年第3期422-426,共5页Journal of Shandong Agricultural University：Natural Science Edition

基　　金：国家自然科学基金(11701337,5227526);山东省自然科学基金(R2022MA009)。

摘　　要：非负矩阵分解问题(nonnegative matrix factorization,NMF)模型已成功应用至高光谱遥感影像处理中的光谱解混工作,由于NMF优化模型具有多个局部极小点,使得分解结果不稳定。设计初始化方法或者选择带正则项的问题模型是提高分解精度的两种常用方法。本文提出了两阶段的NMF算法,实现了初始点选取和正则项设计的结合。第一阶段借助k-均值获得k个聚类中心,给出迭代的初始点;利用第一阶段的初始矩阵U^(0),定义了针对端元矩阵的正则项‖U-U^(0)‖_(F)^(2),第二阶段采用基于交替非负最小二乘框架的投影梯度算法,求解新的正则化NMF问题。正则项中的端元初始矩阵U^(0)除了采用k-均值获得k个聚类中心,也可采用真实地物光谱,它的引入提高了算法的灵活度。数值结果表明新算法更加稳定,且分解的精确性有效提高。The non-negative matrix factorization (NMF) model has been effectively applied in the hyperspectral unmixing.It is known that the objective function's nonconvexity results in the solution's instability.To address this issue,two main streams of approaches have been proposed.Starting NMF with a reasonable initialization or adding regularized terms to NMF.We propose a two-stages NMF method which combines the initialization method and definition of regularized NMF model.In the first stage,k-means is employed to find the initial end-member matrix.In the second stage,a regularized NMF problem is defined,which makes full use of the initial end-member matrix obtained in the first stage.In our algorithm,the initialization matrix of the end-member matrix in the first stage of our algorithm also contributes to the regularized term.The project gradient method is employed to solve the non-negative least square problems alternatively.Numerical results indicate that the new algorithm works well.

关 键 词：非负矩阵分解 正则项 投影梯度法 光谱解混 

分 类 号：TP221[自动化与计算机技术—检测技术与自动化装置] TP751.1[自动化与计算机技术—控制科学与工程]