Joint low-rank and sparse multiple kernel subspace clustering algorithm
LI Xingfeng1, HUANG Yuqing1, REN Zhenwen2
1. School of Information Engineering, Southwest University of Science and Technology, Mianyang Sichuan 621010, China 2. School of National Defense Science and Technology, Southwest University of Science and Technology, Mianyang Sichuan 621010, China
Abstract:Since the methods of multiple kernel subspace spectral clustering do not consider the problem of noise and relation graph structure, a novel Joint Low-rank and Sparse Multiple Kernel Subspace Clustering algorithm (JLSMKC) was proposed. Firstly, with combination of low-rank and sparse representation for subspace learning, the relation graph obtained the attribute of low-rank and sparse structure. Secondly, a robust multiple kernel low-rank and sparsity constraint model was constructed to reduce the influence of noise on the relation graph and handle the nonlinear structure of data. Finally, the quality of relation graph was enhanced by making full use of the consensus kernel matrix by multiple kernel approach. The experimental results on seven datasets show that the proposed JLSMKC is better than five popular multiple kernel clustering algorithms in ACCuracy (ACC), Normalized Mutual Information (NMI) and Purity. Meanwhile, the clustering time is reduced and the block diagonal quality of relation graph is improved. JLSMKC has great advantages in clustering performance.
1 王卫卫,李小平,冯象初,等.稀疏子空间聚类综述[J].自动化学报,2015,41(8):1373-1384. WANGW W, LIX P, FENGX C, et al. A survey on sparse subspace clustering [J]. Acta Automatica Sinica, 2015, 41(8):1373-1384. 2 章永来,周耀鉴.聚类算法综述[J].计算机应用,2019,39(7):1869-1882. ZHANGY L, ZHOUY J. Review of clustering algorithms [J]. Journal of Computer Applications, 2019, 39(7): 1869-1882. 3 万静,郑龙君,何云斌,等.高维不确定数据的子空间聚类算法[J]. 计算机应用, 2019, 39(11):3280-3287. WANJ, ZHENGL J, HEY B, et al. Subspace clustering algorithm for high dimensional uncertain data [J]. Journal of Computer Applications, 2019, 39(11):3280-3287. 4 DINGS, JIAH, DUM, et al. A semi-supervised approximate spectral clustering algorithm based on HMRF model [J]. Information Sciences, 2018, 429: 215-228. 5 ELHAMIFARE, VIDALR. Sparse subspace clustering [C]// Proceedings of the 2009 IEEE Conference on Computer Vision and Pattern Recognition. Piscataway: IEEE, 2009: 2790-2797. 6 LUC, FENGJ, LINZ, et al. Subspace clustering by block diagonal representation [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2019, 41(2): 487-501. 7 ZHUX, ZHANGS, LIY, et al. Low-rank sparse subspace for spectral clustering [J]. IEEE Transactions on Knowledge and Data Engineering, 2019, 31(8): 1532-1543. 8 LIUG, LINZ, YANS, et al. Robust recovery of subspace structures by low-rank representation [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(1): 171-184. 9 NASIHATKONB, HARTLEYR. Graph connectivity in sparse subspace clustering [C]// Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition. Piscataway: IEEE, 2011: 2137-2144. 10 NASHEDM Z, WALTERG G. General sampling theorems for functions in reproducing kernel Hilbert spaces [J]. Mathematics of Control, Signals and Systems, 1991, 4(4): 363-390. 11 SCHÖLKOPFB, SMOLAA, MüLLERK R. Nonlinear component analysis as a kernel eigenvalue problem [J]. Neural Computation, 1998, 10(5): 1299-1319. 12 DUL, ZHOUP, SHIL, et al. Robust multiple kernel K-means using l2,1-norm [C]// Proceedings of the 24th International Joint Conference on Artificial Intelligence. Menlo Park: AAAI Press, 2015: 3476-3482. 13 HUANGJ, NIEF, HUANGH. A new simplex sparse learning model to measure data similarity for clustering [C]// Proceedings of the 24th International Joint Conference on Artificial Intelligence. Menlo Park: AAAI Press, 2015: 3569-3575. 14 王少华,狄岚,梁久祯.基于核与局部信息的多维度模糊聚类图像分割算法[J].计算机应用,2015,35(11):3227-3231,3237. WANGS H, DIL, LIANGJ Z. Multi-dimensional fuzzy clustering image segmentation algorithm based on kernel metric and local information [J]. Journal of Computer Applications, 2015, 35(11): 3227-3231, 3237. 15 HUANGH C, CHUANGY Y, CHENC S. Multiple kernel fuzzy clustering [J]. IEEE Transactions on Fuzzy Systems, 2011, 20(1): 120-134. 16 XUZ, JINR, KINGI, et al. An extended level method for efficient multiple kernel learning [C]// Proceedings of the 21st International Conference on Neural Information Processing Systems. Red Hook: Curran Associates Inc., 2008: 1825-1832. 17 KANGZ, LUX, YIJ, et al. Self-weighted multiple kernel learning for graph-based clustering and semi-supervised classification[C]// Proceedings of the 27th International Joint Conference on Artificial Intelligence. Menlo Park: AAAI Press, 2018: 2312-2318. 18 KANGZ, PENGC, CHENGQ, et al. Unified spectral clustering with optimal graph [C]// Proceedings of the 32nd AAAI Conference on Artificial Intelligence. Menlo Park: AAAI Press, 2018: 3366-3373. 19 KANGZ, WENL, CHENW, et al. Low-rank kernel learning for graph-based clustering [J]. Knowledge-Based Systems, 2019, 163: 510-517. 20 LIUG, LINZ, YUY. Robust subspace segmentation by low-rank representation [EB/OL]. [2019-01-11].http://people.eecs.berkeley.edu/~yima/matrix-rank/Files/lrr.pdf. 21 ELHAMIFARE, VIDALR. Sparse subspace clustering: algorithm, theory, and applications [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(11): 2765-2781. 22 BECKA. On the convergence of alternating minimization for convex programming with applications to iteratively reweighted least squares and decomposition schemes [J]. SIAM Journal on Optimization, 2015, 25(1): 185-209.