联合低秩稀疏的多核子空间聚类算法

doi:10.11772/j.issn.1001-9081.2019111991

计算机应用 ›› 2020, Vol. 40 ›› Issue (6): 1648-1653.DOI: 10.11772/j.issn.1001-9081.2019111991

联合低秩稀疏的多核子空间聚类算法

李杏峰¹, 黄玉清¹, 任珍文²

1.西南科技大学信息工程学院，四川绵阳 621010
2.西南科技大学国防科技学院，四川绵阳 621010

收稿日期:2019-11-25 修回日期:2019-12-27 发布日期:2020-06-18 出版日期:2020-06-10
通讯作者: 黄玉清(1962—)
作者简介:李杏峰(1993—)，男，四川自贡人，硕士研究生，主要研究方向：机器学习、多核聚类.黄玉清(1962—)，女，四川绵阳人，教授，博士，主要研究方向：信号特征提取与识别、图像处理、压缩感知.任珍文(1987—)，男，四川绵阳人，讲师，博士，CCF会员，主要研究方向：多核聚类、多视图聚类、非负矩阵分解、压缩感知。
基金资助:
国家自然科学基金资助项目（61673220）；国家国防科技工业局项目(JCKY2017209B010，JCKY2018209B001)。

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

Received:2019-11-25 Revised:2019-12-27 Online:2020-06-18 Published:2020-06-10
Contact: HUANG Yuqing,born in 1962,Ph. D.,professor. Her research interests include signal feature extraction and recognition,image processing,compressive sensing.
About author:LI Xingfeng，born in 1993，M. S. candidate. His research interests include machine learning，multiple kernel clustering.HUANG Yuqing，born in 1962，Ph. D.，professor. Her research interests include signal feature extraction and recognition，image processing，compressive sensing.REN Zhenwen，born in 1987，Ph. D.，lecturer. His research interests include multiple kernel clustering，multiple view clustering，nonneg?ative matrix factorization，compressive sensing.
Supported by:
National Natural Science Foundation of China (61673220), the Project of State Administration of Science, Technology and Industry for National Defence， PRC (JCKY2017209B010, JCKY2018209B001).

摘要/Abstract

摘要： 针对多核子空间谱聚类算法没有考虑噪声和关系图结构的问题，提出了一种新的联合低秩稀疏的多核子空间聚类算法(JLSMKC)。首先，通过联合低秩与稀疏表示进行子空间学习，使关系图具有低秩和稀疏结构属性；其次，建立鲁棒的多核低秩稀疏约束模型，用于减少噪声对关系图的影响和处理数据的非线性结构；最后，通过多核方法充分利用共识核矩阵来增强关系图质量。7个数据集上的实验结果表明，所提算法JLSMKC在聚类精度(ACC)、标准互信息(NMI)和纯度(Purity)上优于5种流行的多核聚类算法，同时减少了聚类时间，提高了关系图块对角质量。该算法在聚类性能上有较大优势。

关键词: 低秩稀疏, 关系图结构, 子空间学习, 多核, 谱聚类

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.

Key words: low-rank and sparse, relation graph structure, subspace learning, multiple kernel, spectral clustering

中图分类号:

TP301.6

李杏峰, 黄玉清, 任珍文. 联合低秩稀疏的多核子空间聚类算法[J]. 计算机应用, 2020, 40(6): 1648-1653.

LI Xingfeng, HUANG Yuqing, REN Zhenwen. Joint low-rank and sparse multiple kernel subspace clustering algorithm[J]. Journal of Computer Applications, 2020, 40(6): 1648-1653.

参考文献

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.

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联合低秩稀疏的多核子空间聚类算法

Joint low-rank and sparse multiple kernel subspace clustering algorithm

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