Abstract To extract the spatio-temporal information in sequential data effectively, a sequential subspace clustering method via joint lp/l2,p-norms minimization is proposed. Firstly, a l2,p-norm temporal graph is constructed to describe local similarity along the temporal direction by defining the sample-distance dependent weights. Secondly, since non-convex lp-norm(0<p<1) minimization delivers better results than convex l1-norm minimization does, and it removes more links between semantically-unrelated samples, lp-norm is adopted to measure the sparsity of representation matrix. Finally, the linearized alternating direction method is employed to solve the optimization model. Experiments on video dataset, motion dataset, and face dataset confirm the effectiveness of the proposed method.
Fund:Supported by National Natural Science Foundation of China(No.61863001, 61962003, 11661007, 61702244, 11761010), Natural Science Foundation of Jiangxi Province(No.20181BAB202021, 20192BAB205086), The Innovation Special Fund of Graduate of Jiangxi Province(No.YC2019-S393), Research Fund of Gannan Normal University(No.18zb04,YCX18B001)
Corresponding Authors:
YI Yun, Ph.D., lecturer. His research interests include computer vision and video content analysis.
About author:: HU Wenyu, Ph.D., associate professor. His research interests include machine lear-ning and tensor computation. LI Shenghao, master student. His research interests include machine learning and computer vision. TU Zhihui, master student. His research interests include machine learning and computer vision.
[1] ELDAR Y C, MISHALI M. Robust Recovery of Signals from a Structured Union of Subspaces. IEEE Transactions on Information Theory, 2009, 55(11): 5302-5316. [2] HONG W, WRIGHT J, HUANG K, et al. Multiscale Hybrid Linear Models for Lossy Image Representation. IEEE Transactions on Image Processing, 2006, 15(12): 3655-3671. [3] HO J, YANG M H, LIM J, et al. Clustering Appearances of Objects under Varying Illumination Conditions // Proc of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2003: 11-18. [4] FAVARO P, VIDAL R, RAVICHANDRAN A. A Closed Form Solution to Robust Subspace Estimation and Clustering // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2011: 1801-1807. [5] RAO S K, TRON R, VIDAL R, et al. Motion Segmentation in the Presence of Outlying, Incomplete, or Corrupted Trajectories. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010, 32(10): 1832-1845. [6] LI S, LI K, FU Y. Temporal Subspace Clustering for Human Motion Segmentation // Proc of the IEEE International Conference on Computer Vision. Washington, USA: IEEE, 2015: 4453-4461. [7] BRADLEY P S, MANGASARIAN O L. K-Plane Clustering. Journal of Global Optimization, 2000, 16(1): 23-32 [8] VIDAL R, MA Y, SASTRY S. Generalized Principal Component Analysis. IEEE Transactions on Pattern Analysis and Machine Inte-lligence, 2005, 27(12): 1945-1959. [9] JOAO P C, KANADE T. A Multibody Factorization Method for Independently Moving Objects. International Journal of Computer Vision, 1998, 29(3): 159-179. [10] MA Y, DERKSEN H, HONG W, et al. Segmentation of Multivariate Mixed Data via Lossy Data Coding and Compression. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29(9): 1546-1562 [11] LU C Y, MIN H, ZHAO Z Q, et al. Robust and Efficient Subspace Segmentation via Least Squares Regression // Proc of the European Conference on Computer Vision. Berlin, Germany: Springer, 2012: 347-360. [12] 郑建炜,路 程,秦梦洁,等.联合特征选择和光滑表示的子空间聚类算法.模式识别与人工智能, 2018, 31(5): 409-418. (ZHENG J W, LU C, QIN M J, et al. Subspace Clustering via Joint Feature Selection and Smooth Representation.Pattern Recognition and Artificial Intelligence, 2018, 31(5): 409-418.) [13] SHI J B, MALIK J. Normalized Cuts and Image Segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(8): 888-905. [14] NG A Y, JORDAN M I, WEISS Y. On Spectral Clustering: Ana-lysis and an Algorithm // Proc of the 14th International Conference on Neural Information Processing Systems: Natural and Synthetic. Washington, USA: IEEE, 2002: 849-856. [15] ELHAMIFAR E, VIDAL R. Sparse Subspace Clustering // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2009: 2790-2797. [16] 王卫卫,李小平,冯象初,等.稀疏子空间聚类综述.自动化学报, 2015, 41(8): 1373-1384. (WANG W W, LI X P, FENG X C, et al. A Survey on Sparse Subspace Clustering. Acta Automatica Sinica, 2015, 41(8): 1373-1384.) [17] LIU G C, LIN Z C, YU Y. Robust Subspace Segmentation by Low-Rank Representation // Proc of the 27th International Conference on Machine Learning. New York, USA: ACM, 2010: 663-670. [18] DONOHO D L. For Most Large Underdetermined Systems of Linear Equations: The Minimal l1-norm Solution Is Also the Sparsest Solution. Communications on Pure and Applied Mathematics, 2016, 59(6): 797-829. [19] FOUCART S, LAI M J. Sparsest Solutions of Underdetermined Linear Systems via lq-minimization for 0≤q≤1. Applied and Computational Harmonic Analysis, 2009, 26(3): 395-407. [20] LERMAN G, ZHANG T. Robust Recovery of Multiple Subspaces by Geometric lp Minimization. The Annals of Statistics, 2011, 39(5): 2686-2715 [21] ZHAO M B, ZHANG H J, CHENG W L, et al. Joint lp- and l2,p- Norm Minimization for Subspace Clustering with Outlier Pursuit // Proc of the International Joint Conference on Neural Networks. Washington, USA: IEEE, 2016: 3658-3665. [22] ZHANG Z, ZHAO M B, LI F Z, et al. Robust Alternating Low-Rank Representation by Joint lp- and l2,p-norm Minimization. Neural Networks, 2017, 96: 55-70. [23] ZHANG T, TANG Z M, LIU Q. Robust Subspace Clustering via Joint Weighted Schatten-p Norm and lqNorm Minimization. Journal of Electronic Imaging, 2017, 26(3). DOI: 10.1117/1.JEI.26.3.033021. [24] ZHANG X J, XU C, SUN X L, et al. Schatten-q Regularizer Constrained Low Rank Subspace Clustering Model. Neurocomputing, 2016, 182: 36-47. [25] JIANG W, LIU J, QI H, et al. Robust Subspace Segmentation via Nonconvex Low Rank Representation. Information Sciences, 2016, 340/341: 144-158. [26] TANG K W, LIU R S, SU Z X, et al. Structure-Constrained Low-Rank Representation. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(12): 2167-2179. [27] LU C Y, FENG J S, LIN Z C, et al. Correlation Adaptive Subspace Segmentation by Trace Lasso // Proc of the IEEE International Conference on Computer Vision. Washington, USA: IEEE, 2013: 1345-1352 [28] GUO Y, GAO J B, LI F. Spatial Subspace Clustering for Hyperspectral Data Segmentation // Proc of the 3rd International Confe-rence on Digital Information Processing and Communications. New York, USA: IEEE, 2013: 180-190 [29] TIERNEY S, GAO J B, GUO Y. Subspace Clustering for Sequential Data // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2014: 1019-1026. [30] NIE F P, WANG H, HUANG H, et al. Unsupervised and Semi-supervised Learning via l1-norm Graph // Proc of the International Conference on Computer Vision. Washington, USA: IEEE, 2011: 2268-2273. [31] CANDÈS E J, WAKIN M B, BOYD S P, et al. Enhancing Sparsity by Reweighted Minimization. Journal of Fourier Analysis and Applications, 2008, 14(5): 877-905. [32] TANG K W, ZHANG J, SU Z X, et al. Bayesian Low-Rank and Sparse Nonlinear Representation for Manifold Clustering. Neural Processing Letters, 2016, 44(3): 719-733. [33] TANG K W, SU Z X, JIANG W, et al. Superpixels for Large Dataset Subspace Clustering. Neural Computing and Applications, 2018, 31(11). DOI: 10.1007/s00521-018-3914-2. [34] TOMASI C, MANDUCHI R. Bilateral Filtering for Gray and Color Images // Proc of the 6th International Conference on Computer Vision. Washington, USA: IEEE, 1998, 839-846. [35] LIN Z C, LIU R S, SU Z X. Linearized Alternating Direction Method with Adaptive Penalty for Low-Rank Representation // TAYLOR-SHAWE J, ZEMEL R S, BARTLETT P L, et al., eds. Advances in Neural Information Processing Systems 24. Cambridge, USA: The MIT Press, 2011: 612-620. [36] LIN Z C, LIU R S, LI H. Linearized Alternating Direction Method with Parallel Splitting and Adaptive Penalty for Separable Convex Programs in Machine Learning. Machine Learning, 2015, 99: 287-325. [37] SHE Y Y. An Iterative Algorithm for Fitting Nonconvex Penalized Generalized Linear Models with Grouped Predictors. Computational Statistics and Data Analysis, 2012, 56(10): 2976-2990 [38] NIE F P, WANG H, HUANG H, et al. Joint Schatten p-norm and lp-norm Robust Matrix Completion for Missing Value Recovery. Knowledge and Information Systems, 2015, 42(3): 525-544. [39] 赵 剑,吴小俊,董文华.局部约束加强的最小二乘回归子空间聚类.模式识别与人工智能, 2017, 30(10): 943-951. (ZHAO J, WU X J, DONG W H. Locality Constraint Enhanced Least Squares Regression Subspace Clustering. Pattern Recognition and Artificial Intelligence, 2017, 30(10): 943-951.) [40] XIE S N, GIRSHICK R, DOLLAR P, et al. Aggregated Residual Transformations for Deep Neural Networks // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2017: 5987-5995. [41] SHANG F H, CHENG J, LIU Y Y, et al. Bilinear Factor Matrix Norm Minimization for Robust PCA: Algorithms and Applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2018, 40(9): 2066-2080.
2020, Vol. 33 
