基于局部图拉普拉斯约束的鲁棒低秩表示聚类方法

李波; 卢春园; 冷成财; 金连宝

doi:10.16383/j.aas.2015.c150031

基于局部图拉普拉斯约束的鲁棒低秩表示聚类方法

doi: 10.16383/j.aas.2015.c150031

1.
南昌航空大学数学与信息科学学院南昌 330063

基金项目:

国家自然科学基金(61262050,61562062,61363048,61363049),江西省自然科学基金(20151BAB211006)资助

详细信息

作者简介:
卢春园南昌航空大学数学与信息科学学院硕士研究生.主要研究方向为图像处理及数据分析.E-mail:lun_chunyuan@sina.com

冷成财南昌航空大学数学与信息科学学院讲师.主要研究方向为医学图像处理.E-mail:70587@nchu.edu.cn

金连宝南昌航空大学数学与信息科学学院硕士研究生.主要研究方向为图像处理及数据分析.E-mail:jin_lianbao@sina.com

通讯作者:
李波南昌航空大学数学与信息科学学院副教授.主要研究方向为计算机图形学及图像处理.本文通信作者.E-mail:libo@nchu.edu.cn

计量
- 文章访问数: 1962
- HTML全文浏览量: 144
- PDF下载量: 1419
- 被引次数: 0
出版历程
- 收稿日期: 2015-02-04
- 修回日期: 2015-07-16
- 刊出日期: 2015-11-20

Robust Low Rank Subspace Clustering Based on Local Graph Laplace Constraint

1.
School of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063

Funds:

Supported by National Natural Science Foundation of China (61262050, 61562062, 61363048, 61363049) and Natural Science Foundation of Jiangxi Province (20151BAB211006)

摘要

摘要: 针对传统低秩表示聚类方法存在的稀疏性不足及噪声敏感等问题,提出了一种基于局部图拉普拉斯约束的鲁棒低秩表示聚类模型. 一方面,通过加入图像数据局部相似性的约束,在保持表示矩阵分块对角的特性下,增强了其稀疏性;另一方面,从数据相关性的角度分析了低秩表示模型的聚类性质, 通过采用鲁棒低秩表示模型,不仅降低了噪声的干扰,而且减弱了表示字典数据之间的线性相关性,从理论上保证了最终的邻接矩阵具有分块对角的良好聚类性质. 与传统低秩表示方法相比,本文得到的表示矩阵既保证了分块性质,又更加稀疏,仿真实验结果表明聚类效果有明显提升.
- 低秩聚类 /
- 数据聚类 /
- 图拉普拉斯 /
- 鲁棒主成分分析
Abstract: Low rank clustering is one of the state-of-art subspace clustering algorithm, but it suffers from dense adjacency map and noise. In this paper, we propose a robust low rank clustering algorithm based on the local graph laplace constraint, which enhances the sparsity of the adjacency matrix while maintain the clustering characteristic; on the other hand, we analyze the mechanics of clustering from the view of incoherence, and argue that the robust model proposed in this paper not only reduce the noise level, but also lower the coherence between data. Finally, experimental results show that our algorithm is more robust and more effective.
- Low rank clustering /
- data clustering /
- graph Laplace /
- robust principle component analysis (RPCA)

HTML全文

参考文献(26)

[1]	Liu Ping-Ping, Zhao Hong-Wei, Zang Xue-Bai, Dai Jin-Bo. A fast local feature description algorithm. Acta Automatica Sinica, 2010, 36(1):40-45(刘萍萍, 赵宏伟, 臧雪柏, 戴金波. 一种快速局部特征描述算法. 自动化学报, 2010, 36(1):40-45)
[2]	Yu Wang-Sheng, Tian Xiao-Hua, Hou Zhi-Qiang, Huang An-Qi, Liu Xiang. Visual tracking algorithm based on feature matching of key regions. Acta Electronica Sinica, 2014, 42(11):2150-2156(余旺盛, 田孝华, 侯志强, 黄安奇, 刘翔. 基于关键区域特征匹配的视觉跟踪算法. 电子学报, 2014, 42(11):2150-2156)
[3]	Zeng Hui, Mu Zhi-Chun, Wang Xiu-Qing. A robust method for local image feature region description. Acta Automatica Sinica, 2011, 37(6):658-664(曾慧, 穆志纯, 王秀青. 一种鲁棒的图像局部特征区域的描述方法. 自动化学报, 2011, 37(6):658-664)
[4]	Chen Shu-Rong, Li Bo, Dong Rong, Chen Qi-Mei. Contourlet-SIFT feature matching algorithm. Journal of Electronics and Information Technology, 2013, 35(5):1215-1221(陈抒瑢, 李勃, 董蓉, 陈启美. Contourlet-SIFT特征匹配算法. 电子与信息学报, 2013, 35(5):1215-1221)
[5]	Lin Hai-Feng, Ma Yu-Feng, Song Tao. Research on object tracking algorithm based on SIFT. Acta Automatica Sinica, 2010, 36(8):1204-1208(蔺海峰, 马宇峰, 宋涛. 基于SIFT特征目标跟踪算法研究. 自动化学报, 2010, 36(8):1204-1208)
[6]	Ye Lin, Chen Yue-Lin, Lin Jing-Liang. Pedestrian fast detection based on histograms of oriented gradient. Computer Engineering, 2010, 36(22):206-210(叶林, 陈岳林, 林景亮. 基于HOG的行人快速检测. 计算机工程, 2010, 36(22):206-210)
[7]	Guo Jin-Xin, Chen Wei. Face recognition based on HOG multi-feature fusion and random forest. Computer Science, 2013, 40(10):279-282(郭金鑫, 陈玮. 基于HOG多特征融合与随机森林的人脸识别. 计算机科学, 2013, 40(10):279-282)
[8]	Tong Ying. Facial expression recognition algorithm based on spatial multi-scaled HOG feature. Computer Engineering and Design, 2014, 35(11):3918-3922, 3979(童莹. 基于空间多尺度HOG特征的人脸表情识别方法. 计算机工程与设计, 2014, 35(11):3918-3922, 3979)
[9]	[9] Wright J, Yang A Y, Ganesh A, Sastry S S, Ma Y. Robust face recognition via sparse representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 31(2):210-227
[10]	Elhamifar E, Vidal R. Sparse subspace clustering:algorithm, theory, and applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(11):2765-2781
[11]	Yang Rong-Gen, Ren Ming-Wu, Yang Jing-Yu. Sparse representation based face recognition algorithm. Computer Science, 2010, 37(9):267-269, 278(杨荣根, 任明武, 杨静宇. 基于稀疏表示的人脸识别方法. 计算机科学, 2010, 37(9):267-269, 278)
[12]	Vidal R, Favaro P. Low rank subspace clustering (LRSC). Pattern Recognition Letters, 2014, 43:47-61
[13]	Liu G C, Lin Z C, Yan S C, Sun J, Yu Y, Ma Y. Robust recovery of subspace structures by low-rank representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(1):171-184
[14]	Shi Jia-Rong, Zheng Xiu-Yun, Wei Zong-Tian, Yang Wei. Survey on algorithms of low-rank matrix recovery. Application Research of Computers, 2013, 30(6):1601-1605(史加荣, 郑秀云, 魏宗田, 杨威. 低秩矩阵恢复算法综述. 计算机应用研究, 2013, 30(6):1601-1605)
[15]	Shi J, Malik J. Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(8):888-905
[16]	Peng Yi-Gang, Suo Jin-Li, Dai Qiong-Hai, Xu Wen-Li. From compressed sensing to low-rank matrix recovery:theory and applications. Acta Automatica Sinica, 2013, 39(7):981-994(彭义刚, 索津莉, 戴琼海, 徐文立. 从压缩传感到低秩矩阵恢复:理论与应用. 自动化学报, 2013, 39(7):981-994)
[17]	Wei S M, Yu Y Z. Subspace segmentation with a minimal squared frobenius norm representation. In:Proceedings of the 21st International Conference on Pattern Recognition (ICPR). Tsukuba:IEEE, 2012. 3509-3512
[18]	Cands E, Li X D, Ma Y, Wright J. Robust principal component analysis? Journal of the ACM, 2011, 58(3):Article No. 11
[19]	Liu G C, Li P. Recovery of coherent data via low-rank dictionary pursuit. Advances in Neural Information Processing Systems, 2014, 27:1206-1214
[20]	Boyd S, Parikh N, Chu E, Peleato B, Eckstein J. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 2011, 3(1):1-122
[21]	Parikh N, Boyd S. Proximal algorithms. Foundations and Trends in Optimization, 2014, 1(3):123-231
[22]	Cai J F, Cands E J, Shen Z W. A singular value thresholding algorithm for matrix completion. SIAM Journal on Optimization, 2010, 20(4):1956-1982
[23]	Lu C Y, Min H, Zhao Z Q, Zhu L, Huang D S, Yan S C. Robust and efficient subspace segmentation via least squares regression. Computer VisionECCV 2012. Berlin Heidelberg:Springer, 2012. 347-360
[24]	Yan J Y, Pollefeys M. A general framework for motion segmentation:independent, articulated, rigid, non-rigid, degenerate and non-degenerate. Computer VisionECCV 2006. Berlin, Heidelberg:Springer, 2006. 94-106
[25]	Zhang H Y, Lin Z C, Zhang C, Gao J B. Robust latent low rank representation for subspace clustering. Neurocomputing, 2014, 145:369-373
[26]	Liu G C, Yan S C. Latent low-rank representation for subspace segmentation and feature extraction. In:Proceedings of the 2011 IEEE International Conference on Computer Vision (ICCV). Barcelona:IEEE, 2011. 1615-1622