|
|
Weighted Block Subspace Clustering Based on Least Square Regression |
LI Hui, CHEN Xiaoyun |
College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116 |
|
|
Abstract Traditional subspace clustering algorithms need to transform each sample into a vector form. Therefore, problems of high dimensionality and small size samples are caused, the natural structural information of each sample is ignored and the clustering information is missing. To overcome the drawbacks, the weighted block subspace clustering based on least square regression algorithm (WB-LSR) is proposed. Firstly, each sample is divided into lots of blocks, and the corresponding affinity matrices of each block are obtained. Next, the weight of each affinity matrix is determined by mutual vote between affinity matrices. Finally, the weighted sum of affinity matrices is regarded as final affinity matrix. The experimental results on image datasets and motion segmentation video datasets show that the proposed method effectively improves clustering accuracy.
|
Received: 11 March 2016
|
|
Fund:Supported by National Natural Science Foundation of China (No.11571074,71273053), Natural Science Foundation of Fujian Province (No.2014J01009) |
About author:: (LI Hui, born in 1989, master student. His research interests include data mining and pattern recognition.) (CHEN Xiaoyun(Corresponding author), born in 1970, Ph.D., professor. Her research interests include data mining and pattern recognition.) |
|
|
|
[1] BOULT T E, BROWN L G. Factorization-Based Segmentation of Motions // Proc of the IEEE Workshop on Visual Motion. Washingtion, USA: IEEE, 1991: 179-186. [2] WU Y, ZHANG Z Y, HUANG T S, et al. Multibody Grouping via Orthogonal Subspace Decomposition // Proc of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2001, II: 252-257. [3] VIDAL R, MA Y, SASTRY S. Generalized Principal Component Analysis (GPCA). IEEE Trans on Pattern Analysis and Machine Intelligence, 2005, 27(12): 1945-1959. [4] RAO S R, YANG A Y, SASTRY S S, et al. Robust Algebraic Segmentation of Mixed Rigid-Body and Planar Motions from Two Views. International Journal of Computer Vision, 2010, 88(3): 425-446. [5] 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 Re-cognition. Washington, USA: IEEE, 2003, I: 11-18. [6] BRADLEY P S, MANGASARIAN O L. k-Plane Clustering. Journal of Global Optimization, 2000, 16(1): 23-32. [7] FISCHLER M A, BOLLES R C. Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography. Communications of the ACM, 1981, 24(6): 381-395. [8] TIPPING M E, BISHOP C M. Mixtures of Probabilistic Principal Component Analyzers. Neural Computation, 1999, 11(2): 443-482. [9] VON LUXBURG U. A Tutorial on Spectral Clustering. Statistics and Computing, 2007, 17(4): 395-416. [10] LAUER F, SCHN RR C. Spectral Clustering of Linear Subspaces for Motion Segmentation // Proc of the 12th IEEE International Conference on Computer Vision. Washington, USA: IEEE, 2009: 678-685. [11] 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.) [12] ELHAMIFAR E, VIDAL R. Sparse Subspace Clustering: Algorithm, Theory and Applications. IEEE Trans on Pattern Analysis and Machine Intelligence, 2013, 35(11): 2765-2781. [13] LIU G C, LIN Z C, YU Y. Robust Subspace Segmentation by Low-Rank Representation[C/OL]. [2016-02-20]. http://icml2010.haifa.il.ibm.com/papers/521.pdf. [14] 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. [15] SAHA B, PHAM D S, PHUNG D, et al. Sparse Subspace Clus-tering via Group Sparse Coding[C/OL]. [2016-02-20]. http://epubs.siam.org/doi/pdf/10.1137/1.9781611972832.15. [16] FENG J S, LIN Z C, XU H, et al. Robust Subspace Segmentation with Block-Diagonal Prior // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2014: 3818-3825. [17] VIDAL R, FAVARO P. Low Rank Subspace Clustering (LRSC). Pattern Recognition Letters, 2014, 43: 47-61. [18] CHEN J, YI Z. Subspace Clustering by Exploiting a Low-Rank Representation with a Symmetric Constraint[J/OL]. [2016-02-20]. http://101.96.10.62/arxiv.org/pdf/1403.2330v2.pdf. [19] LI C G, VIDAL R. Structured Sparse Subspace Clustering: A Unified Optimization Framework // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2015: 277-286. [20] 陈晓云,陈慧娟.潜在最小二乘回归子空间分割方法.模式识别与人工智能, 2016, 29(1): 31-38. (CHEN X Y, CHEN H J. Latent Least Square Regression for Subspace Segmentation. Pattern Recognition and Artificial Intelligence, 2016, 29(1): 31-38.) [21] SHI J B, MALIK J. Normalized Cuts and Image Segmentation. IEEE Trans on Pattern Analysis and Machine Intelligence, 2000, 22(8): 888-905. [22] CAI D, HE X F, WU X Y, et al. Non-negative Matrix Factorization on Manifold // Proc of the 8th IEEE International Conference on Data Mining. Washington, USA: IEEE, 2008: 63-72. [23] CHEN S S, DONOHO D L, SAUNDERS M A. Atomic Decomposition by Basis Pursuit. SIAM Review, 2001, 43(1): 129-159. |
|
|
|