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| Lanczos双对角化:一种快速的非负矩阵初始化方法 | |
| 引用本文： | 王炫盛,陈震,卢琳璋.Lanczos双对角化:一种快速的非负矩阵初始化方法[J].厦门大学学报(自然科学版),2012,51(2):149-152. |
| 作者姓名： | 王炫盛 陈震 卢琳璋 |
| 作者单位： | 1. 厦门大学数学科学学院,福建厦门,361005 2. 贵州师范大学数学与计算机科学学院,贵州贵阳,550001 3. 厦门大学数学科学学院,福建厦门361005;贵州师范大学数学与计算机科学学院,贵州贵阳550001 |
| 基金项目： | 国家自然科学基金项目(10961010);贵州省科学技术基金项目(黔科合J字LKS[2009]03号) |
| 摘 要： | 对于大型的非负矩阵,利用Lanczos双对角化得到了一个低秩近似.类似于Boutsidis Gallopoulos的方法,可以进一步得到它的非负近似,由此得到了非负矩阵分解的一种新的初始化方法.它虽然带有一点随意性,但可以和已有的非负矩阵分解方法相结合.从数值试验可以看出,与基于奇异值分解的初始化方法相比较,该初始化方法更加有效. |
| 关 键 词： | Lanczos双对角化 非负矩阵分解 奇异值分解 低秩近似 |
Lanczos Bidiagonalization:a Fast Start for Nonnegative Matrix Factorization |
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| WANG Xuan-sheng , CHEN Zhen , LU Lin-zhang.Lanczos Bidiagonalization:a Fast Start for Nonnegative Matrix Factorization[J].Journal of Xiamen University(Natural Science),2012,51(2):149-152. | |
| Authors: | WANG Xuan-sheng CHEN Zhen LU Lin-zhang |
| Institution: | 1,2*(1.School of Mathematical Sciences,Xiamen University,Xiamen 361005,China; 2.School of Mathematics and Computer Science,Guizhou Normal University,Guiyang 550001,China) |
| Abstract: | For a lage nonnegative matrix,a Lanczos bidiagonalization process is utilized to obtain a nonnegative bidiagonal matrix of low rank,and then every unit rank matrix produced from the Lanczos process is approximated by its nonnegative section in the same way as developed in Boutsidis and Gallopoulos′s paper.This results in a novel initialization algorithm for nonnegative matrix factorization(NMF) can readily be combined with existing NMF algorithms and may contained a little randomization.Some numerical experiments demonstrate that the new initialization algorithm is more efficient than the SVD based initialization algorithm presented in Boutsidis and Gallopoulos′s paper. |
| Keywords: | Lanczos bidiagonalization nonnegative matrix factorization singular value decomposition low-rank approximation |
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