分块NMF及其在图像压缩中的应用

陈剑军

摘 要 基于矩阵乃“局部构成整体”的思想和并行计算的模式，将矩阵分块进行非负矩阵分解，并将其用于图像压缩。实验表明：该方法可减少存储量、计算量，计算量的减少较为显著。

关键词 矩阵分块 矩阵Hadamard乘积 NMF 图像压缩

中图分类号：TN911.73 文献标识码：A DOI：10.16400/j.cnki.kjdkx.2016.09.066

Abstract Based on the idea of "local integral whole" and the parallel computing model， the matrix is divided into non negative matrix factorization， and it is used for image compression. Experimental results show that this method can reduce the amount of storage and computation， and the computation is more significant.

Key words Matrix block； matrix； Hadamard product； NMF； image compression

参考文献

[1] Lee D.D，Seung H.S.Learning the parts of objects by non-negative matrix factorization[J].Nature， 1999， 401 （6755）：788-791.

[2] CHENG Ming-song，LIU Shao-lian.A Practical Fast NMF Algorithm[J].Journal of Dalian University of Technology，2013，53（1）： 151-156.

[3] GAO Hong-tao.Study on Theory and its Application of Non-negative Matrix Factorization Algorithm[D]. Shanghai： Tongji University.2005：8-18.

[4] WANG Xuan-sheng，CHEN Zheng，LU Lin-zhang. Lanczos Bidiagonalization： A Fast Start for Non-negative Matrix Factorization [J].Journal of Xiamen University（Natural Science），2012，51（2）：149-152.

[5] XU Sen，LU Zhi-mao，GU Guo-chang.Integrating K-Means and Non-negative Matrix Factorization to Ensemble Document Clustering [J].Journal of Jinlin University（Engineering and Technology Edition），2011，41（4）：149-152.

[6] LI Le，ZHANG Yu-jin.A Survey of Non-negative Matrix Factorization[J]. ACTA ELECTRONICA SINICA[J].2008，36（4）：738-743.

[7] XU Tai-yan，HAO Yu-long.The Current Research Situation Analysis of Non-negative Matrix Factorization and Applications[J].Journal of Wuhan Polytechnic University， 2010，29（1）：109-114.

[8] Wild S， Curry J，Dougherty A.Improving non-negative matrix factorization through structured initialization [J].Pattern Recognition， 2004，37（11）： 2217-2232.