大规模非负矩阵分解算法及其在盐湖保护与利用方面的应用研究

项目名称： 大规模非负矩阵分解算法及其在盐湖保护与利用方面的应用研究

项目编号： No.11241005

项目类型： 专项基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 胡运红

作者单位： 运城学院

项目金额： 40万元

中文摘要： 近年来，非负矩阵分解(NMF)理论与算法研究取得了一定的研究成果，并广泛应用于图像处理、机器学习和模式识别、统计特征数据提取与分析等领域。但是NMF算法和应用仍有许多问题需要研究，从而完善NMF理论和算法的进一步应用。本项目拟对NMF的理论和算法进行研究，进而应用于盐湖的保护与利用。(1)应用代数学知识，对非负秩给出其界的估计，进一步给出非负矩阵分解算法的初始点选择策略，改善现有算法的收敛性能；(2)对于大规模问题，采取有效集方法降低约束规模，结合二次凸规划子问题的求解,提出凸和非凸二次规划的NMF算法,弥补已有算法只考虑凸二次规划的不足；(3)利用非负矩阵分解算法对遥感影像信息进行提取，构建盐湖生态质量评价的各项指标体系和评价方法，特别为运城盐湖的保护与合理利用提供科学依据。本项目的研究对NMF算法和广泛的应用具有重要的理论意义和价值。

中文关键词： 非负矩阵分解算法；聚类分析；图像复原；模式识别；低秩分解

英文摘要： In recent years,Nonnegative Matrix Factorization (NMF)method have been widely used in the fields of image processing, machine learning , pattern recognition,and analysis of statistics data.It will have more prosperous applications in more fields. But in some aspects,it has not been explored thoroughly which is vital to the futural applications and will held the futural development of NMF,so it''s necessary and valuable to do some researches on NMF,both on algorithm and application aspects.This proposal plans to do some researches on the following aspects of NMF but not limited to:(1)The rank of the NMF is important in the algorithms and we paln to make an estimation of the rank by albebra knowledges. NMF algorithms play an vital role in the reason that most established algorithms are local algorithms and often effected by the choice of the initial points. We plan to find an effective scheme for most available algorithms by using Shanno entropy information other features of the data;(2)A basic principle to solve large scale problem is to reduce the scale, we plan to reduce the scale of NMF by using active set for the constraints,and persue some convex and nonconvex quadratic algorithms and QP-free algorithms for the reduced NMF problems which will promote the performance of the available algorithms;(3)Using NMF

英文关键词： Nonnegative Matrix Factorizaiton；Clustering；Image restoration；Pattern recognition；Low-rank Factorization