线性投影非负矩阵分解方法及应用  

Application and Method for Linear Projective Non-negative Matrix Factorization

作　　者：胡俐蕊[1,2,3] 吴建国[2,3] 汪磊[2,3] 

机构地区：[1]南通大学计算机科学与技术学院,南通226019 [2]安徽大学计算智能与信号处理教育部重点实验室,合肥230039 [3]安徽大学计算机科学与技术学院,合肥230039

出　　处：《计算机科学》2013年第10期269-273,共5页Computer Science

基　　金：安徽省科技攻关项目(07010202057)资助

摘　　要：针对线性投影结构非负矩阵分解迭代方法比较复杂的问题,提出了一种线性投影非负矩阵分解方法。从投影和线性变换角度出发,将Frobenius范数作为目标函数,利用泰勒展开式,严格导出基矩阵和线性变换矩阵的迭代算法,并证明了算法的收敛性。实验结果表明:该算法是收敛的;相对于非负矩阵分解等方法,该方法的基矩阵具有更好的正交性和稀疏性;人脸识别结果说明该方法具有较高的识别率。线性投影非负矩阵分解方法是有效的。To solve the problem that the iterative method for Linear Projection-Based Non-negative Matrix Factorization （LPBNMF） is complex, a method, called Linear Projective Non-negative Matrix Factorization（LP-NMF）, was proposed. In LP-NMF, from projection and linear transformation angle, an objective function of Frobenius norm is considered. The Taylor series expansion is used. An iterative algorithm for basis matrix and linear transformation matrix is derived strictly and a proof of algorithm convergence is provided. Experimental results show that the algorithm is convergent, and relative to Non-negative Matrix Factorization（NMF）and so on, the orthogonality and the sparseness of the basis matrix are better, in face recognition, there is higher recognition accuracy. The method for LP-NMF is effective.

关 键 词：投影非负矩阵分解 线性变换 人脸识别 

分 类 号：TP39[自动化与计算机技术—计算机应用技术]