一种改进的最小二乘回归子空间分割方法
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摘要
最小二乘回归(LSR)算法是一种常见的子空间分割方法,由于LSR具有解析解,因此它的聚类性能较高。然而LSR算法是应用谱聚类方法聚类数据,谱聚类方法初始化聚类中心是随机的,会影响后面的聚类效果。针对这一问题,提出一种基于聚类中心局部密度和距离这2个特点的改进的LSR算法(LSR-DC)。在Extended Yale B数据集上进行实验,结果表明,该算法有较高的聚类精度,具有一定的鲁棒性,优于现有LSR等子空间分割方法。
Least Squares Regression(LSR) is a common approach for subspace segmentation, it is very efficient due to a closed form solution. However, spectral clustering is exploited in LSR to obtain the final segmentation results. The drawback of spectral clustering is that it randomly initializes the cluster centers, which may undermine the subsequent clustering performance. In order to tackle this problem, this paper presents an improved LSR algorithm(LSR-DC) based on two characteristics of cluster centers, i.e. local density and distance. Experimental results on the Extended Yale B database show that LSR-DC is robust and is superior to the existing LSR subspace segmentation methods.
Least Squares Regression(LSR) is a common approach for subspace segmentation, it is very efficient due to a closed form solution. However, spectral clustering is exploited in LSR to obtain the final segmentation results. The drawback of spectral clustering is that it randomly initializes the cluster centers, which may undermine the subsequent clustering performance. In order to tackle this problem, this paper presents an improved LSR algorithm(LSR-DC) based on two characteristics of cluster centers, i.e. local density and distance. Experimental results on the Extended Yale B database show that LSR-DC is robust and is superior to the existing LSR subspace segmentation methods.
引文
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[13] 薛以梅.基于稀疏表示和梯度先验的图像盲去模糊[J].计算机与现代化,2017(12):39-42.
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[15] ELHAMIFAR E,VIDAL R.Sparse subspace clustering:Algorithm,theory,and applications[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2013,35(11):2765-2781.
[16] 邹臣嵩,刘松.基于谱聚类的全局中心快速更新聚类算法[J].计算机与现代化,2018(10):6-11.
[17] LIU G,LIN Z,YAN S,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.
[18] FAVARO P,VIDAL R,RAVICHANDRAN A.A closed form solution to robust subspace estimation and clustering[C]// IEEE Conference on Computer Vision and Pattern Recognition (CVPR).2011:1801-1807.
[19] CHEN Y,ZHANG L,ZHANG Y.A novel low rank representation algorithm for subspace clustering[J].International Journal of Pattern Recognition and Artificial Intelligence,2016,30(4):1650007.
[20] LU C Y,MIN H,ZHAO Z Q,et al.Robust and efficient subspace segmentation via least squares regression[C]// European Conference on Computer Vision (ECCV).2012:347-360.
[21] RODRIGUEZ A,LAIO A.Clustering by fast search and find of density peaks[J].Science,2014,344(6191):1492-1496.
[22] ZOU H,HASTIE T.Regularization and variable selection via the elastic net[J].Journal of the Royal Statistical Society:Series B (Statistical Methodology),2005,67(2):301-320.
[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[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2001,23(6):643-660.
[2] CHEN J,YANG J.Robust subspace segmentation via low-rank representation[J].IEEE Transactions on Cybernetics,2014,44(8):1432-1445.
[3] VIDAL R.A tutorial on subspace clustering[J].IEEE Signal Processing Magazine,2011,28(2):52-68.
[4] AGRAWAL R,GEHRKE J,GUNOPULOS D,et al.Automatic subspace clustering of high dimensional data for data mining applications[J].ACM SIGMOD Record,1998,27(2):94-105.
[5] LU L,VIDAL R.Combined central and subspace clustering for computer vision applications[C]// Proceedings of the 23rd International Conference on Machine Learning(ICML).2006:593-600.
[6] YANG A Y,WRIGHT J,MA Y,et al.Unsupervised segmentation of natural images via lossy data compression[J].Computer Vision and Image Understanding,2008,110(2):212-225
[7] LIU G,LIN Z,YU Y.Robust subspace segmentation by low-rank representation[C]// Proceedings of the 27th International Conference on Machine Learning (ICML).2010:663-670.
[8] LIU G C,YAN S C.Latent low-rank representation for subspace segmentation and feature extraction[C]// Proceedings of 2011 IEEE International Conference on Computer Vision(ICCV).2011:1615-1622.
[9] LU C Y,MIN H,ZHAO Z Q,et al.Robust and efficient subspace segmentation via least squares regression[C]// The 12th European Conference on Computer Vision(ECCV).2012:347-360.
[10] 陈晓云,陈慧娟.潜在最小二乘回归子空间分割方法[J].模式识别与人工智能,2016,29(1):31-38.
[11] WRIGHT J,YANG A Y,GANESH A,et al.Robust face recognition via sparse representation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2009,31(2):210-227.
[12] 那天,宋晓宁,於东军.基于主元分析和线性判别分析降维的稀疏表示分类[J].南京理工大学学报(自然科学版),2018,42(3):286-291.
[13] 薛以梅.基于稀疏表示和梯度先验的图像盲去模糊[J].计算机与现代化,2017(12):39-42.
[14] ZHANG L,YANG M,FENG X C.Sparse representation or collaborative representation:Which helps face recognition?[C]// IEEE International Conference on Computer Vision(ICCV).2011:471-478.
[15] ELHAMIFAR E,VIDAL R.Sparse subspace clustering:Algorithm,theory,and applications[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2013,35(11):2765-2781.
[16] 邹臣嵩,刘松.基于谱聚类的全局中心快速更新聚类算法[J].计算机与现代化,2018(10):6-11.
[17] LIU G,LIN Z,YAN S,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.
[18] FAVARO P,VIDAL R,RAVICHANDRAN A.A closed form solution to robust subspace estimation and clustering[C]// IEEE Conference on Computer Vision and Pattern Recognition (CVPR).2011:1801-1807.
[19] CHEN Y,ZHANG L,ZHANG Y.A novel low rank representation algorithm for subspace clustering[J].International Journal of Pattern Recognition and Artificial Intelligence,2016,30(4):1650007.
[20] LU C Y,MIN H,ZHAO Z Q,et al.Robust and efficient subspace segmentation via least squares regression[C]// European Conference on Computer Vision (ECCV).2012:347-360.
[21] RODRIGUEZ A,LAIO A.Clustering by fast search and find of density peaks[J].Science,2014,344(6191):1492-1496.
[22] ZOU H,HASTIE T.Regularization and variable selection via the elastic net[J].Journal of the Royal Statistical Society:Series B (Statistical Methodology),2005,67(2):301-320.
[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[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2001,23(6):643-660.