Abstract：In the existing non-negative matrix factorization(NMF) methods, low-dimensional repre-sentation is directly computed on the original high-dimensional image dataset. Besides, NMF methods are sensitive to noise data, noise labels, unreliable graphs and poor in robustness. To solve these problems, a non-negative low rank graph embedding algorithm based on L21 norm(NLGEL21) is proposed. NLGEL21 takes the effective low rank structure and geometric information of the original dataset into account. L21 norm is introduced into the function of graph embedding and data reconstruction to further improve its robustness. In addition, a multiplicative iteration formula and convergence proof for NLGEL21 are produced. Experiments on ORL, CMU PIE and YaleB face databases show the superiority of NLGEL21.
[1] WU J X, ZHONG S H, JIANG J M, et al. A Novel Clustering Method for Static Video Summarization. Multimedia Tools and Applications, 2017, 76(7): 9625-9641. [2] CHEN J Y, ZHENG H B, LIN X, et al. A Novel Image Segmentation Method Based on Fast Density Clustering Algorithm. Enginee-ring Applications of Artificial Intelligence, 2018, 73: 92-110. [3] 姜 波,叶灵耀,潘伟丰,等.基于需求功能语义的服务聚类方法.计算机学报, 2018, 41(6): 1255-1266. (JIANG B, YE L Y, PAN W F, et al. Service Clustering Based on the Functional Semantics of Requirements. Chinese Journal of Computers, 2018, 41(6): 1255-1266.) [4] YE R Z, LI X L. Compact Structure Hashing via Sparse and Similarity Preserving Embedding. IEEE Transactions on Cybernetics, 2016, 46(3): 718-729. [5] TAO D, JIN L, YANG Z, et al. Rank Preserving Sparse Learning for Kinect Based Scene Classification. IEEE Transactions on Cybernetics, 2013, 43(5): 1406-1417. [6] FANG X Z, XU Y, LI X L, et al. Locality and Similarity Preserving Embedding for Feature Selection. Neurocomputing, 2014, 128: 304-315. [7] ZHU X F, LI X L, ZHANG S C. Block-Row Sparse Multiview Multilabel Learning for Image Classification. IEEE Transactions on Cybernetics, 2016, 46(2): 450-461. [8] LEE D D, SEUNG H S. Learning the Parts of Objects by Non-negative Matrix Factorization. Nature, 1999, 401(6755): 788-791. [9] LEE D D, SEUNG H S. Algorithms for Non-negative Matrix Factorization // Proc of the 13th International Conference on Neural Information Processing Systems 12. Cambridge, USA: The MIT Press, 2000: 535-541. [10] CAI D, HE X F, HAN J W, et al. Graph Regularized Non-negative Matrix Factorization for Data Representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011, 33(8): 1548-1560. [11] LI X L, CUI G S, DONG Y S. Graph Regularized Non-negative Low-Rank Matrix Factorization for Image Clustering. IEEE Transactions on Cybernetics, 2017, 47(11): 3840-3853. [12] 杜海顺,张旭东.图嵌入正则化投影非负矩阵分解人脸图像特征提取.中国图象图形学报, 2014, 19(8): 1176-1184. (DU H S, ZHANG X D. Graph Embedding Regularized Projective Non-negative Matrix Factorization for Face Image Feature Extraction. Journal of Image and Graphics, 2014, 19(8): 1176-1184.) [13] WEN J, FANG X Z, XU Y, et al. Low-Rank Representation with Adaptive Graph Regularization. Neural Networks, 2018, 108: 83-96. [14] 刘 正,张国印,陈志远.基于特征加权和非负矩阵分解的多视角聚类算法.电子学报, 2016, 44(3): 535-540. (LIU Z, ZHANG G Y, CHEN Z Y. A Multiview Clustering Algorithm Based on Feature Weighting and Non-negative Matrix Factorization. Acta Electronica Sinica, 2016, 44(3): 535-540. [15] YIN M, GAO J B, LIN Z C. Laplacian Regularized Low-Rank Representation and Its Applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2016, 38(3): 504-517. [16] WANG J Z, ZHAO R, WANG Y, et al. Locality Constrained Graph Optimization for Dimensionality Reduction. Neurocompu-ting, 2017, 245: 55-67. [17] MENG Y, SHANG R H, JIAO L C, et al. Dual-Graph Regula-rized Non-negative Matrix Factorization with Sparse and Orthogonal Constraints. Engineering Applications of Artificial Intelligence, 2018, 69: 24-35. [18] XIAO S J, TAN M K, XU D, et al. Robust Kernel Low-Rank Representation. IEEE Transactions on Neural Networks and Lear-ning Systems, 2016, 27(11): 2268-2281. [19] 万 源,陈晓丽,张景会,等.低秩稀疏图嵌入的半监督特征选择.中国图象图形学报, 2018, 23(9): 1316-1325. (WAN Y, CHEN X L, ZHANG J H, et al. Semi-supervised Feature Selection Based on Low-Rank Sparse Graph Embedding. Journal of Image and Graphics, 2018, 23(9): 1316-1325.) [20] YAN S C, XU D, ZHANG B Y, et al. Graph Embedding and Extensions: A General Framework for Dimensionality Reduction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29(1): 40-51. [21] YANG J C, YANG S C, FU Y, et al. Non-negative Graph Embe-dding //Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2008. DOI: 10.1109/CVPR.2008.4587665. [22] ZHANG H W, ZHA Z J, YANG Y, et al. Robust (Semi) Non-negative Graph Embedding. IEEE Transactions on Image Proce-ssing, 2014, 23(7): 2996-3012. [23] ZHOU T Y, TAO D C. GoDec: Randomized Low-Rank & Sparse Matrix Decomposition in Noisy Case[C/OL]. [2018-12-22]. http://www.icml-2011.org/papers/41_icmlpaper.pdf. [24] ROWEIS S. EM Algorithms for PCA and SPCA // JORDAN M I, KEARNS M J, SOLLA S A, eds. Advances in Neural Information Processing Systems 10. Cambridge, USA: The MIT Press, 1997: 626-632. [25] LIU X B, YAN S C, JIN H. Projective Non-negative Graph Embedding. IEEE Transactions on Image Processing, 2010, 19(5): 1126-1137. [26] WOLD S, ESBENSEN K, GELADI P. Principal Component Ana-lysis. Chemometrics and Intelligent Laboratory Systems, 1987, 2(1/2/3): 37-52. [27] HE X F, NIYOGI P. Locality Preserving Projections // THRUN S, SAUL L K, SCHOLKOP B, eds. Advances in Neural Information Processing Systems 16. Cambridge, USA: The MIT Press, 2003: 153-160. [28] LI S Z, HOU X W, ZHANG H J, et al. Learning Spatially Loca-lized, Parts-Based Representation // Proc of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2001. DOI: 10.1109/CVPR.2001.990477. [29] FISHER R A. The Statistical Utilization of Multiple Measurements. Annals of Eugenics, 1938, 8(4): 376-386.
2019, Vol. 32 
