Abstract The coefficient matrix solved by sparse subspace clustering(SSC) is too sparse and the coefficient matrix solved by least squares regression for subspace clustering(LSR) is too dense. Aiming at these problems, subspace clustering based on collaborative representation(SCCR) is proposed. The advantages of SSC and LSR are combined. The l1 norm and the Frobenius norm are introduced into an objective function. The coefficient solved by SCCR can group the correlated data within cluster like LSR and eliminate the connection between clusters like SSC. Then, the affinity matrix constructed by this coefficient matrix is applied to spectral clustering. The experimental results demonstrate that SCCR improves the performance of clustering.
Fund:Supported by National Natural Science Foundation of China(No.61672265,61373055), Industrialization Project of Jiangsu Educational Department(No.JH10-28), Production and Research Innovation Project of Jiangsu Province(No.BY2012059)
About author:: FU Wenjin, born in 1992, master student. His research interests include cluster analysis. WU Xiaojun(Corresponding author), born in 1967, Ph.D., professor. His research interests include artificial intelligence, pattern recognition and computer vision. DONG Wenhua, born in 1975, Ph.D.candidate, lecturer. His research interests include artificial intelligence and pattern recognition. YIN Hefeng, born in 1989, Ph.D. candidate. His research interests include sparse representation based classification and low rank matrix recovery.
[1] VIDAL R, MA Y, SASTRY S. Generalized Principal Component Analysis(GPCA). IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(12): 1945-1959. [2] 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. [3] LU L, VIDAL R. Combined Central and Subspace Clustering for Computer Vision Applications // Proc of the 23rd International Conference on Machine Learning. New York, USA: ACM, 2006: 593-600. [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] COSTEIRA J P, KANADE T. A Multibody Factorization Method for Independently Moving Objects. International Journal of Computer Vision, 1998, 29(3): 159-179. [6] 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. [7] YAN J Y, POLLEFEYS M. A General Framework for Motion Segmentation: Independent, Articulated, Rigid, Non-rigid, Degene-rate and Non-degenerate // Proc of the 9th European Conference on Computer Vision. Berlin, Germany: Springer, 2006: 94-106. [8] GOH A, VIDAL R. Segmenting Motions of Different Types by Unsupervised Manifold Clustering // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2007. DOI: 10.1109/CVPR.2007.383235. [9] ELHAMIFAR E, VIDAL R. Sparse Subspace Clustering: Algorithm, Theory, and Applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(11): 2765-2781. [10] LU C Y, MIN H, ZHAO Z Q, et al. Robust and Efficient Subspace Segmentation via Least Squares Regression // Proc of the 12th European Conference on Computer Vision. Berlin, Germany: Springer, 2012: 347-360. [11] LIU G C, LIN Z C, YAN S C, et al. Robust Recovery of Subspace Structures by Low-Rank Representation. IEEE Transactions on Pa-ttern Analysis and Machine Intelligence, 2013, 35(1): 171-184. [12] LU C Y, FENG J, 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. [13] BOYD S, PARIKH N, CHU E, et al. Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. Foundations and Trends in Machine Learning, 2011, 3(1): 1-122. [14] PHAM D S, BUDHADITYA S, PHUNG D, et al. Improved Subspace Clustering via Exploitation of Spatial Constraints // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2012: 550-557. [15] XU J, XU K, CHEN K, et al. Reweighted Sparse Subspace Clustering. Computer Vision and Image Understanding, 2015, 138: 25-37. [16] CAI D, HE X F, HAN J W, et al. Graph Regularized Nonnegative Matrix Factorization for Data Representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011, 33(8): 1548-1560. [17] CANDE/S E J, WAKIN M B, BOYD S P. Enhancing Sparsity by Reweighted l1 Minimization. Journal of Fourier Analysis and Applications, 2008, 14(5): 877-905. [18] BERTSEKAS D P. Constrained Optimization and Lagrange Multiplier Methods. New York, USA: Academic Press, 2014. [19] ZHANG Y. Recent Advances in Alternating Direction Methods: Practice and Theory[C/OL]. [2016-05-21]. http://helper.ipam.ucia.edu/publications/opws2/opws2_9066.pdf. [20] TRON R, VIDAL R. A Benchmark for the Comparison of 3-D Motion Segmentation Algorithms // Proc of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Wa-shington, USA: IEEE, 2007. DOI: 10.1109/CVPR.2007.382974. [21] BROX T, MALIK J. Object Segmentation by Long Term Analysis of Point Trajectories // Proc of the 11th European Conference on Computer Vision. Berlin, Germany: Springer, 2010: 282-295. [22] OCHS P, MALIK J, BROX T. Segmentation of Moving Objects by Long Term Video Analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2014, 36(6): 1187-1200. [23] GEORGHIADES A S, BELHUMEUR P N, KRIEGMAN D J. From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(6): 643-660. [24] ZHAO Y, KARYPIS G. Criterion Functions for Document Clus-tering: Experiments and Analysis. Technical Report, 01-40. Minneapolis, USA: University of Minnesota, 2001. [25] HU H, LIN Z C, FENG J J, et al. Smooth Representation Clus-tering // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2014: 3834-3841. [26] LUO D J, NIE F P, DING C, et al. Multi-subspace Representation and Discovery // Proc of the Joint European Conference on Machine Learning and Knowledge Discovery in Databases. Berlin, Germany: Springer, 2011: 405-420.
2017, Vol. 30 
