|
|
Sparse Regularized Non-Negative Matrix Factorization through Online Learning |
XUE Mo-Gen1,2,XU Guo-Ming1,2,WANG Feng2 |
1. School of Computer and Information,Hefei University of Technology,Hefei 230009 2.Army Officer Academy of PLA,Hefei 230031 |
|
|
Abstract In order to overcome the inefficiency of non-negative matrix factorization,a fast approach based on online learning for sparse regularized non-negative matrix factorization is proposed. Firstly,the objective function is defined by imposing the regularization term to control the sparsity of the coefficient matrix,and the problem is transformed into the dictionary learning problem of sparse representation. Therefore,the object function can be solved by the online dictionary learning algorithm. Then,the block-coordinate descent algorithm is used to update the matrix in every iterative process,consequently,the convergence rate is improved. The experimental results show that the proposed method effectively preserves the structure information of images and simultaneously enhances the running efficiency evidently.
|
Received: 14 November 2011
|
|
|
|
|
[1] Lee D D,Seung H S. Learning the Parts of Objects by Non-Negative Matrix Factorization. Nature,1999,401(21): 788-791 [2] Lee D D,Seung H S. Algorithms for Non-Negative Matrix Factorization // Leen T K,Dietterich T G,Tresp V,eds. Advances in Neural Information Processing Systems. Cambridge,USA: MIT Press,2001,XIII: 556-562 [3] Li Le,Zhang Yujin. A Survey on Algorithms of Non-Negative Matrix Factorization. Acta Electronica Sinica,2008,36(4): 737-743 (in Chinese) (李 乐,章毓晋.非负矩阵分解算法综述.电子学报,2008,36(4): 737-743) [4] Cichocki A,Amari S I,Zdunek R,et al. Extended SMART Algorithms for Non-negative Matrix Factorization // Proc of the 8th International Conference on Artificial Intelligence and Soft Computing. Zakopane,Poland,2006: 548-562 [5] Hoyer P O. Non-negative Sparse Coding // Proc of the 12th IEEE Workshop on Neural Networks for Signal Processing. Martigny,Switzerland,2002: 557-565 [6] Liu Weixiang,Zheng Nanning,Lu Xiaofeng. Non-Negative Matrix Factorization for Visual Coding // Proc of the IEEE International Conference on Acoustics,Speech and Signal Processing. Hong Kong,China,2003,III: 293-296 [7] Hoyer P O. Non-Negative Matrix Factorization with Sparseness Constraints. Journal of Machine Learning Research,2004,5(11): 1457-1469 [8] Heiler M,Schnorr C. Learning Sparse Representations by Non-Negative Matrix Factorization and Sequential Cone Programming. Journal of Machine Learning Research,2006,7(7): 1385-1407 [9] Pascual-Montano A,Carzzo J M,Kochi K,et al. Nonsmooth Non-Negative Matrix Factorization(nsNMF). IEEE Trans on Pattern Analysis and Machine Intelligence,2006,28(3): 403-415 [10] Mairal J,Bach F,Ponce J,et al. Online Learning for Matrix Factorization and Sparse Coding. Journal of Machine Learning Research,2010,11(1): 19-60 [11] Cai Lei,Zhu Yongsheng.Time-Frequency Spectra Recognition Based on Sparse Non-Negative Matrix Factorization and Support Vector Machine. Acta Automatica Sinica,2009,35(10): 1272-1277 (in Chinese) (蔡 蕾,朱永生.基于稀疏性非负矩阵分解和支持向量机的时频图像识别.自动化学报,2009,35(10): 1272-1277) [12] Yang Jingyu,Peng Yigang,Xu Wenli,et al. Ways to Sparse Representation: An Overview. Science China: Information Science,2009,52(4): 695-703 [13] Rubinstein R,Brucksteir A M,Elad M. Dictionaries for Sparse Representation Modeling. IEEE Trans on Signal Process,2010,98(6): 1045-1057 [14] Efron B,Hastie T,Johnstone I,et al. Least Angle Regression. Annals of Statistics,2004,32(2): 407-499 [15] Tseng P. Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization. Journal of Optimization Theory and Applications,2001,109(3): 475-494 [16] Tseng P,Yun S. Block-Coordinate Gradient Descent Method for Linearly Constrained Nonsmooth Separable Optimization. Journal of Optimization Theory and Applications,2009,140(3): 513-535 [17] Zhou Pucheng,Han Yusheng,Xue Mogeng,et al. Polarization Image Fusion Approach Based on Non-Negative Matrix Factorization and IHS Color Model. Acta Photonica Sinica,2010,39(9): 1682-1687(in Chinese) (周浦城,韩裕生,薛模根,等.基于非负矩阵分解和IHS颜色模型的偏振图像融合方法.光子学报,2010,39(9): 1682-1687) |
|
|
|