计算机应用 ›› 2012, Vol. 32 ›› Issue (05): 1362-1365.

• 人工智能 • 上一篇    下一篇

基于光滑性和主成分的非负矩阵分解算法

马鹏1,杨丹2,方蔚涛3,葛永新2,张小洪2   

  1. 1. 重庆大学 数学与统计学院,重庆 401331
    2. 重庆大学 软件学院,重庆 401331
    3. 重庆大学 计算机学院,重庆 400030
  • 收稿日期:2011-11-07 修回日期:2011-12-27 发布日期:2012-05-01 出版日期:2012-05-01
  • 通讯作者: 马鹏
  • 作者简介:马鹏(1986-),男,山东枣庄人,硕士研究生,主要研究方向:子空间学习算法;杨丹(1962-),男,重庆开县人,教授,博士生导师,主要研究方向:模式识别、人工智能;方蔚涛(1975-),男,安徽淮南人,博士研究生,主要研究方向:数字图像处理;葛永新(1981-),男,江苏镇江人,讲师,博士,主要研究方向:模式识别、人工智能;张小洪(1973-),男,四川大竹人,教授,博士,主要研究方向:模式识别、人工智能。
  • 基金资助:

    国家自然科学基金资助项目(61074145);重庆市科技攻关重点项目(CSTC2009AB2230);教育部博士点基金资助项目(20090191110023)

Smoothness and principal components based non-negative matrix factorization

MA Peng1,YANG Dan2,FANG Wei-tao3,GE Yong-xin2,ZHANG Xiao-hong2   

  1. 1. College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China
    2. School of Software Engineering, Chongqing University, Chongqing 401331,China
    3. College of Computer Science, Chongqing University, Chongqing 400030,China
  • Received:2011-11-07 Revised:2011-12-27 Online:2012-05-01 Published:2012-05-01
  • Contact: MA Peng

摘要: 非负矩阵分解(NMF)存在收敛速度慢的缺点,其根本原因是基图像(基矩阵)包含大量的噪声点。另外,系数矩阵相关性很大,不利于区分不同图像。鉴于以上缺点,提出了基于光滑性和主成分的非负矩阵分解(SPNMF):一方面通过添加常数矩阵来增强基矩阵的光滑性,平抑噪声点,达到减少迭代次数的目的;另一方面在原损失函数基础上,将系数矩阵不同列之间的方差作为惩罚项,提高系数矩阵的区分度。在PIE和FERET人脸库中的实验表明,SPNMF不仅能够提高人脸识别的正确率,而且速度比NMF快2~4倍,使得基于非负矩阵的人脸识别系统更具有实用价值。

关键词: 非负矩阵分解, 主成分分析, 光滑性, 人脸识别

Abstract: Non-negative Matrix Factorization (NMF) has the disadvantage of slow convergence, which is mainly due to that the base image (base matrix) contains lots of noise points. Besides, the coefficient matrix is significantly dependent, which is not conducive to distinguish between different images. In view of the above shortcomings, a new algorithm called Smoothness and Principal Components Based Non-Negative Matrix Factorization (SPNMF) was proposed in this paper. SPNMF had two novelties. On one hand, a constant matrix was added to the base matrix to enhance the smoothness and stabilize the noise points, which caused good convergence; on the other hand, to improve the discrimination, the variance between the different columns of the coefficient matrix as a penalty term was added to the loss function of NMF. The experimental results on the PIE face database and FERET face database show that the proposed method not only has higher recognition performance compared with the traditional algorithms, but also is two to four times faster than NMF, making the face recognition system based on NMF more practical.

Key words: Non-negative Matrix Factorization (NMF), Principal Component Analysis (PCA), smoothness, face recognition

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