计算机科学 ›› 2015, Vol. 42 ›› Issue (7): 280-284.doi: 10.11896/j.issn.1002-137X.2015.07.060

• 人工智能 • 上一篇    下一篇

基于稀疏约束的半监督非负矩阵分解算法

胡学考,孙福明,李豪杰   

  1. 辽宁工业大学电子与信息工程学院 锦州121001,辽宁工业大学电子与信息工程学院 锦州121001,大连理工大学软件学院 大连116300
  • 出版日期:2018-11-14 发布日期:2018-11-14
  • 基金资助:
    本文受国家自然科学基金(61272214,9)资助

Constrained Nonnegative Matrix Factorization with Sparseness for Image Representation

HU Xue-kao, SUN Fu-ming and LI Hao-jie   

  • Online:2018-11-14 Published:2018-11-14

摘要: 矩阵分解因可以实现大规模数据处理而具有十分广泛的应用。非负矩阵分解(Nonnegative Matrix Factorization,NMF)是一种在约束矩阵元素为非负的条件下进行的分解方法。利用少量已知样本的标注信息和大量未标注样本,并施加稀疏性约束,构造了一种新的算法——基于稀疏约束的半监督非负矩阵分解算法。推导了其有效的更新算法,并证明了该算法的收敛性。在常见的人脸数据库上进行了验证,实验结果表明CNMFS算法相对于NMF和CNMF等算法具有较好的稀疏性和聚类精度。

关键词: 非负矩阵分解,半监督,稀疏约束

Abstract: Matrix decomposition is widely applied in many domains since it is exploited to process the large-scale data.To the best of our knowledge,nonnegative matrix factorization (NMF) is a non-negative decomposition method under the condition that constraint matrix elements are non-negative.By using the informati on provided by a few known labeled examples and large number of unlabeled examples as well as imposing a certain sparseness constraint on NMF, this paper put forward a method called constraint nonnegative matrix factorization with sparseness (CNMFS).In the algorithm,an effective update approach is constructed,whose convergence is proved subsequently.Extensive experiments were conducted on common face databases,and the comparisons with two state-of-the-art algorithms including CNMF and NMF demonstrate that CNMFS has superiority in both sparseness and clustering.

Key words: Nonnegative matrix factorization,Semi-supervised,Sparseness constraints

[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] 杜世强,石玉清,王维兰,等.基于图正则化的半监督非负矩阵分解[J].计算机工程与应用,2012,8(36):194-200Du Shi-qiang,Shi Yu-qing,Wang Wei-lan,et al.Graph regulari-zed-based semi-supervised non-negative matrix factorization [J].Computer Engineering and Applications,2012,48(36):194-200
[3] Cai Deng,He Xiao-fei,Han Jia-wei,et al.Graph regularized non-negative matrix factorization for data representation[J].IEEE Trans on Pattern Anal Mach Intell,2011,33(8):1548-1560
[4] Hoyer P O.Non-negative matrix factorization with sparsenessconstrains[J].Journal of Machine Learning Research,2004,5(9):1457-1469
[5] Sun Fu-ming,Tang Jin-hui,Li Hao-jie,et al.Multi-label image categorization with sparse factor representation [J].IEEE Transaction on Image Processing,2014,23(3):1028-1037
[6] Li S Z,Hou Xin-wen,Zhang Hong-jiang,et al.Learning spatially localized,parts-based representation [C]∥Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.Los Alamitos,California,USA,2001(1):207-212
[7] Liu Hai-feng,Wu Zhao-hui,Li Xue-long,et al.Constrained non-negative matrix factorization for image representation [J].IEEE Trans on Pattern Anal Mach Intell,2012,34(7):1299-1311
[8] Shahnaza F,Berrya M W,Paucab V,et al.Plemmonsb.Docu-ment clustering using nonnegative matrix factorization[J].Information Processing Management,2006,42(2):373-386
[9] Lovasz L,Plummer M.Matching Theory [M].North Holland,1986
[10] Michael W,Shakhina A,Stewart G W.Computing sparse re-duced-rank approximations to sparse matrices [J].ACM Transactions on mathematical software,2004,19(3):231-235

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