基于流形正则化的非光滑非负矩阵分解  

Manifold Regularized-based Nonsmooth Nonnegative Matrix Factorization

作　　者：姜伟[1] 陈耀[1] 杨炳儒[2] 

机构地区：[1]辽宁师范大学数学学院,大连116029 [2]北京科技大学计算机与通信工程学院,北京100083

出　　处：《计算机科学》2014年第3期272-275,共4页Computer Science

基　　金：国家自然科学基金项目(60875029)资助

摘　　要：经典的非光滑非负矩阵分解方法只能发现数据中的全局统计信息,对于非线性分布数据无能为力,而流形学习方法在探索高维非线性数据集真实几何结构方面具有明显优势。鉴于此,基于流形正则化思想,提出了一种新颖的基于流形正则化的非光滑非负矩阵分解方法。该方法不仅考虑了数据的几何结构,而且对编码系数矩阵和基矩阵同时进行稀疏约束,并将它们整合于单个目标函数中。构造了一个有效的乘积更新算法,并在理论上证明了算法的收敛性。标准数据集上的实验表明了MRnsNMF的有效性。The classical Nonsmooth Nonnegative Matrix Factorization（nsNMF） method discovers only the global statistical information of data and fails in dealing with nonlinear distributed data,while the manifold learning algorithms show great power in exploring the faithful intrinsic geometry structures of high dimensional data set.To address this issue,based on manifold regularization,we developed a novel algorithm called Manifold Regularized-based Nonsmooth Nonnegative Matrix Factorization（MRnsNMF）.It not only considers the geometric structure in the data representation,but also introduces sparseness constraint to both coding coefficient and basis matrix simultaneously,and integrates them into one single objective function.An efficient multiplicative updating procedure was produced along with its theoretic justification of the algorithmic convergence.The feasibility and effectiveness of MRnsNMF were verified on several standard data sets with promising results.

关 键 词：非负矩阵分解 非光滑 流形正则化 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]