WU Xi,DU Yuanhua,ZHOU Nan.Tensor Multi-view Subspace Clustering via Maximum Correntropy Criterion[J].Journal of Chengdu University of Information Technology,2024,39(03):389-396.[doi:10.16836/j.cnki.jcuit.2024.03.018]
基于最大相关熵的张量多视图子空间聚类
- Title:
- Tensor Multi-view Subspace Clustering via Maximum Correntropy Criterion
- 文章编号:
- 2096-1618(2024)03-0389-08
- Keywords:
- maximum correntropy criterion(MCC); tensor; multi-view; block coordinate descent; clustering
- 分类号:
- O183.2
- 文献标志码:
- A
- 摘要:
- 由于多个视图能够更加全面、恰当地描述数据信息,对多视图子空间聚类(MVSC)算法研究的热度愈加高涨。将最大相关熵准则引入到张量多视图聚类,并在块坐标下降求解框架下提出一个新的多视图子空间聚类算法,称为基于最大相关熵准则的张量多视图子空间聚类(TMVSC-MCC)算法。提出的优化模型将所有视图的子空间表示矩阵视作一个三阶张量。通过对张量施加低秩约束与引入最大相关熵准则的度量使所提出的模型不仅能够通过张量低秩约束充分挖掘视图间的高阶相关信息,并通过最大相关熵准则的度量消除多视图数据中噪声的影响。由于提出模型的非凸性,利用加速块坐标下降算法对模型进行有效求解。为验证TMVSC-MCC算法的性能,在4个图像数据集上进行对比实验,结果证实所提出的算法优于其他9种聚类算法。
- Abstract:
- Multiple views can describe data information comprehensively and appropriately, which makes the research on multi-view subspace clustering(MVSC) algorithm more popular. This paper proposes a new multi-view subspace clustering algorithm, called tensor multi-view subspace clustering via maximum correntropy(TMVSC-MCC). Our method treats the subspace representation matrix of all views as a third-order tensor. By imposing low rank constraints on a tensor and introducing maximum correntropy criterion,the proposed model fully exploits high-order correlation information between views, and eliminates the impact of noise in multi-view data. Due to the non convexity, the accelerated block coordinate descent algorithm can solve the problem effectively. We make comparative experiments on four image datasets, and the results show that the proposed algorithm is superior to the other nine clustering algorithms.
参考文献/References:
[1] Vidal R.Subspace clustering[J].IEEE Signal Process,2011,28(2):52-68.
[2] Jia H,Ding S,Du M.A Nyström spectral clustering algorithm based on probability incremental sampling[J].Soft Computing:A Fusion of Foundations,Methodologies and Applications,2017,21(19):5815-5827.
[3] Ding S,Jia H,Du M,et al.A semi-supervised approximate spectral clustering algorithm based on HMRF model[J].Information Sciences:An International Journal,2018,429(3):215-228.
[4] Ding S,Cong L,Hu Q,et al.A multiway p-spectral clustering algorithm[J].Knowledge-Based Systems,2019,164(1):371-377.
[5] Elhamifar E,Vidal R.Sparse subspace clustering:algorithm,theory,and applications[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2012,35(11):2765-2781.
[6] 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.
[7] Vidal R,Favaro P.Low rank subspace clustering(LRSC)[J].Pattern Recognition Letters,2014,43(1):47-61.
[8] Zhu W,Lu J,Zhou J.Nonlinear subspace clustering for image clustering[J].Pattern Recognitio Letters,2018,107(5):131-136.
[9] Xia R,Pan Y,Du L,et al.Robust multi-view spectral clustering via low-rank and sparse decomposition[C].AAAI Conference on Artificial Intelligence.Québec,2017:2149-2155.
[10] Zhang C,Fu H,Liu S,et al.Low-rank tensor constrained multiview subspace clustering[C].IEEE International Conference on Computer Vision.Santiago, 2015:1582-1590.
[11] Cao X,Zhang C,Fu H,et al.Diversity induced multi-view subspace clustering[C].IEEE Computer Vision and Pattern Recognition.Boston,2015:586-594.
[12] Xie Y,Tao D,Zhang W,et al.On unifying multi-view self-representations for clustering by tensor multi-tank minimization[J].International Journal of Computer Vision,2018,126(11):1157-1179.
[13] Wu J,Lin Z,Zha H.Essential tensor learning for multi-view spectral clustering[J].IEEE Transactions on Image Processing,2019,28(12):5910-5922.
[14] Zhang C,Fu H,Wang J,et al.Tensorized multi-view subspace representation learning[J].International Journal of Computer Vision,2020,128(8):2344-2361.
[15] Gao H,Nie F,Li X,et al.Multi-view subspace clustering[C].IEEE International Conference on Computer Vision.Sanntiago,2015:4238-4246.
[16] Li R,Zhang C,Hu Q,et al.Flexible multi-view representation learning for subspace clustering[C].International Joint Conference on Artificial Intelligence,2019.
[17] Zhang C,Hu Q,Fu H,et al.Latent multi-view subspace clustering[C].IEEE Conference on Computer Vision and Pattern Recognition.Hawaii,2017:4333-4341.
[18] Misha E,Kilmer C,Martin D.Factorization strategies for thirdorder tensors[J].Linear Algebra and its Applications,2011,435(3):641-658.
[19] Zhang Z,Ely G,Aeron S,et al.Novel methods for multilinear data completion and de-noising based on Tensor-SVD[C].IEEE Conference on Computer Vision and Pattern Recognition.Columbus,2014:3842-3849.
[20] Ng A Y,Jordan M I,Weiss Y.On spectral clustering:Analysis and an algorithm[C].Conference and Workshop on Neural Information Processing Systems,2001.
[21] Liu J,Musialski P,Wonka P,et al.Tensor completion for estimating missing values in visual data[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2013,35(1):208-220.
[22] Tomioka R,Hayashi K,Kashima H.Estimation of low-rank tensors via convex optimization[J/OL].https://10.48550/arXiv.1010.0789,2010-10-05.
[23] DeL L,De M B,Vandewalle J.A multilinear singular value decomposition[J].SIAM Journal on Matrix Analysis and Applications,2000,21(4):1253-1278.
[24] DeL L,De M B,Vandewalle J.On the best rank-1 and rank-(r1,r2,...,rn)approximation of higherorder tensors[J].SIAM Journal on Matrix Analysis and Applications,2000,21(4):1324-1342.
[25] Zhou N,Chen B D,Du Y H,et al.Maximum correntropy criterion-based robust semisupervised concept factorization for image representation[J].IEEE Transactions on Neural Networks and Learning Systems,2020,31(10):3877-3891.
[26] Rockafellar R T.Convex analysis[J/OL].https://press.princeton.edu/books/ebook/9781400873173,2015-04-29.
[27] Xu Y,Yin W.A block coordinate descent method for regularized multiconvex optimization with applications to nonnegative tensor factorization and completion[J].SIAM Journal on Imaging Sciences,2013,6(3):1758-1789.
[28] Lin Z,Liu R,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.
[29] Cao X,Wei X,Han Y,et al.Robust tensor clustering with non-greedy maximization[C].Association for the Advancement of Artificial Intelligence,2013.
[30] Chen Y,Tao C,Bai Q,et al.Short-term speed prediction for expressway considering adaptive selection of spatiotemporal dimensions and similar rraffic features[J].Journal of Transportation Engineering,2020(10):146.
[31] Kumar A,Rai P,Daume H.Co-regularized multi-view spectral clustering[C].Conference and Workshop on Neural Information Processing Systems,2011.
[32] Sa V.Spectral clustering with two views[C].International Conference on Machine Learning,2005.
[33] Collins M D,Liu J,Xu J,et al.Spectral clustering with a convex regularizer on millions of images[C].European Conference on Computer Vision,2014.
[34] Zhao Z,Yan S,Zhao M,et al.Robust bilinear matrix recovery by tensor low-rank representation[C].IEEE International Joint Conference on Neural Networks,2014.
备注/Memo
收稿日期:2022-11-07
基金项目:国家自然科学基金资助项目(11901063)
通信作者:杜元花. E-mail:duyh@cuit.edu.cn