核结构限制的低秩表示及其在流形聚类上的应用
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摘要
针对很多计算机视觉问题中的数据往往具有混合多流形结构,提出一种流形聚类方法.通过对2,1范数采用一种特殊的迭代格式,将结构限制的低秩表示方法进行了核化,解决了其核化存在的技术难题.在Hopkins155和Caltech 256等数据集上的实验结果表明,核结构限制低秩表示是一个有效的流形聚类方法.
Because the data in many computer vision problems usually has the structure of mixing manifolds,a manifold clustering method is proposed in this paper. By designing the special iteration of 2,1 norm to overcome the technical problem, the proposed method kernelizes structure-constrained low-rank representation. Experimental results on Hopkins 155, Caltech 256, etc. confirm the effectiveness of the kernel structure constrained low-rank representation for manifold clustering.
Because the data in many computer vision problems usually has the structure of mixing manifolds,a manifold clustering method is proposed in this paper. By designing the special iteration of 2,1 norm to overcome the technical problem, the proposed method kernelizes structure-constrained low-rank representation. Experimental results on Hopkins 155, Caltech 256, etc. confirm the effectiveness of the kernel structure constrained low-rank representation for manifold clustering.
引文
[1]Wang Huibing,Feng Lin,Wu Zhenyu.A dimension reduction algorithm based on divergence balance[J].Journal of Computer-Aided Design&Computer Graphics,2016,28(6):995-1002(in Chinese)(王辉兵,冯林,吴振宇.一种基于离散度平衡的降维算法[J].计算机辅助设计与图形学学报,2016,28(6):995-1002)
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[9]Tang K W,Liu R S,Su Z X,et al.Structure-constrained low-rank representation[J].IEEE Transactions on Neural Networks and Learning Systems,2014,25(12):2167-2179
[10]Wang Y,Jiang Y,Wu Y,et al.Spectral clustering on multiple manifolds[J].IEEE Transactions on Neural Networks,2011,22(7):1149-1161
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[13]Chen G,Atev S,Lerman G..Kernel spectral curvature clustering[OL].[2018-06-24].https://arxiv.org/abs/0909.1605
[14]Patel V M,Vidal R.Kernel sparse subspace clustering[C]//Proceedings of the IEEE International Conference on Image Processing.Los Alamitos:IEEE Computer Society Press,2014:2849-2853
[15]Yin M,Guo Y,Gao J,et al.Kernel sparse subspace clustering on symmetric positive definite manifolds[C]//Proceedings of the Computer Vision and Pattern Recognition.Los Alamitos:IEEE Computer Society Press,2016:5157-5164
[16]Xiao S J,Tan M K,Xu D,et al.Robust kernel low-rank representation[J].IEEE Transactions on Neural Networks and Learning Systems,2016,27(11):2268-2281
[17]Chen G L,Lerman G.Spectral curvature clustering[J].International Journal of Computer Vision,2009,81(3):317-330
[18]Tang K W,Zhang J,Su Z X,et al.Bayesian low-rank and sparse nonlinear representation for manifold clustering[J].Neural Processing Letters,2016,44(3):719-733
[19]Lin Z C,Chen M M,Ma Y.The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices[OL].[2018-06-24].https://arxiv.org/abs/1009.5055
[20]Ojala T,Pietikainen M,Maenpaa T.Multiresolution gray-scale and rotation invariant texture classification with local binary patterns[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,24(7):971-987
[21]Tron R,Vidal R.A benchmark for the comparison of 3-D motion segmentation algorithms[C]//Proceedings of the IEEEConference on Computer Vision and Pattern Recognition.Los Alamitos:IEEE Computer Society Press,2007,1:1-8
[22]Lowe D G..Object recognition from local scale-invariant features[C]//Proceedings of the International Conference on Computer Vision.Los Alamitos:IEEE Computer Society Press,1999,2:1150-1157
(1)http://sipi.usc.edu/database/database.cgi?volume=textures.
[2]Li Feng,Wang Zhengqun,Zhou Zhongxia,et al.Semi-supervised sparsity preserving two-dimensional marginal Fisher analysis dimensionality reduction algorithm[J].Journal of Computer-Aided Design&Computer Graphics,2014,26(6):923-931(in Chinese)(李峰,王正群,周中侠,等.半监督的稀疏保持二维边界Fisher分析降维算法[J].计算机辅助设计与图形学学报,2014,26(6):923-931)
[3]Basri R,Jacobs D W.Lambertian reflectance and linear subspaces[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2003,25(2):218-223
[4]Wang Y,Jiang Y,Wu Y,et al.Multi-manifold clustering[C]//Proceedings of the 11th Pacific Rim International Conferences on Trends in Artificial Intelligence.Heidelberg:Springer,2010:280-291
[5]Vidal R.Subspace clustering[J].IEEE Signal Processing Magazine,2011,28(2):52-68
[6]Shi J,Malik J.Normalized cuts and image segmentation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2000,22(8):888-905
[7]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
[8]Liu G C,Lin Z C,Yan S C,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]Tang K W,Liu R S,Su Z X,et al.Structure-constrained low-rank representation[J].IEEE Transactions on Neural Networks and Learning Systems,2014,25(12):2167-2179
[10]Wang Y,Jiang Y,Wu Y,et al.Spectral clustering on multiple manifolds[J].IEEE Transactions on Neural Networks,2011,22(7):1149-1161
[11]Tipping M E,Bishop C M.Mixtures of probabilistic principal component analyzers[J].Neural Computation,1999,11(2):443-482
[12]Babaeian A,Bayestehtashk A,Bandarabadi M.Multiple manifold clustering using curvature constrained path[J].PLoS ONE,2015,10(9):e0137986
[13]Chen G,Atev S,Lerman G..Kernel spectral curvature clustering[OL].[2018-06-24].https://arxiv.org/abs/0909.1605
[14]Patel V M,Vidal R.Kernel sparse subspace clustering[C]//Proceedings of the IEEE International Conference on Image Processing.Los Alamitos:IEEE Computer Society Press,2014:2849-2853
[15]Yin M,Guo Y,Gao J,et al.Kernel sparse subspace clustering on symmetric positive definite manifolds[C]//Proceedings of the Computer Vision and Pattern Recognition.Los Alamitos:IEEE Computer Society Press,2016:5157-5164
[16]Xiao S J,Tan M K,Xu D,et al.Robust kernel low-rank representation[J].IEEE Transactions on Neural Networks and Learning Systems,2016,27(11):2268-2281
[17]Chen G L,Lerman G.Spectral curvature clustering[J].International Journal of Computer Vision,2009,81(3):317-330
[18]Tang K W,Zhang J,Su Z X,et al.Bayesian low-rank and sparse nonlinear representation for manifold clustering[J].Neural Processing Letters,2016,44(3):719-733
[19]Lin Z C,Chen M M,Ma Y.The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices[OL].[2018-06-24].https://arxiv.org/abs/1009.5055
[20]Ojala T,Pietikainen M,Maenpaa T.Multiresolution gray-scale and rotation invariant texture classification with local binary patterns[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,24(7):971-987
[21]Tron R,Vidal R.A benchmark for the comparison of 3-D motion segmentation algorithms[C]//Proceedings of the IEEEConference on Computer Vision and Pattern Recognition.Los Alamitos:IEEE Computer Society Press,2007,1:1-8
[22]Lowe D G..Object recognition from local scale-invariant features[C]//Proceedings of the International Conference on Computer Vision.Los Alamitos:IEEE Computer Society Press,1999,2:1150-1157
(1)http://sipi.usc.edu/database/database.cgi?volume=textures.