Soft Computing

, Volume 21, Issue 8, pp 1937–1948 | Cite as

Multi-view spectral clustering via robust local subspace learning



Because of the existence of multiple sources of datasets, multi-view clustering has a wide range of applications in data mining and pattern recognition. Multi-view could utilize complementary information that existed in multiple views to improve the performance of clustering. Recently, there have been multi-view clustering methods which improved the performance of clustering to some extent. However, they do not take local representation relationship into consideration and local representation relationship is a crucial technology in subspace learning. To solve this problem, we proposed a novel multi-view clustering algorithm via robust local representation. We consider that all the views are derived from a robust unified subspace and noisy. To get the robust similarity matrix we simultaneously take all the local reconstruction relationships into consideration and use L1-norm to guarantee the sparsity. We give an iteration solution for this problem and give the proof of correctness. We compare our method with a number of classical methods on real-world and synthetic datasets to show the efficacy of the proposed algorithm.


Multi-view learning Spectral clustering Robust local subspace learning 


  1. Banerjee A, Dhillon I, Ghosh J et al (2003) Generative model-based clustering of directional data. In: Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, pp 19–28Google Scholar
  2. Bickel S, Scheffer T (2004) Multi-view clustering. ICDM 4:19–26Google Scholar
  3. Blaschko MB, Lampert CH (2008) Correlational spectral clustering. Computer Vision and Pattern Recognition CVPR 2008. IEEE Conference on. IEEE, pp 1–8Google Scholar
  4. Blum A, Mitchell T (1998) Combining labeled and unlabeled data with co-training. In: Proceedings of the eleventh annual conference on Computational learning theory. ACM, pp 92–100Google Scholar
  5. Cai D, He X, Han J (2005) Document clustering using locality preserving indexing. IEEE Trans Knowl Data Eng 17(12):1624–1637CrossRefGoogle Scholar
  6. Chaudhuri K, Kakade SM, Livescu K et al (2009) Multi-view clustering via canonical correlation analysis. In: Proceedings of the 26th annual international conference on machine learning. ACM, pp 129-136Google Scholar
  7. Cortes C, Mohri M, Rostamizadeh A (2009) Learning non-linear combinations of kernels. Adv Neural Inform Process Syst:396–404Google Scholar
  8. de Sa VR (2005) Spectral clustering with two views. ICML workshop on learning with multiple views, pp 20–27Google Scholar
  9. Deng C, Lv Z, Liu W et al (2015) Multi-view matrix decomposition: a new scheme for exploring discriminative information. In: Proceedings of the 24th International Conference on Artificial Intelligence. AAAI Press, pp 3438–3444Google Scholar
  10. Ding C, Li T, Jordan M (2010) Convex and semi-nonnegative matrix factorizations. IEEE Trans Pattern Anal Mach Intell 32(1):45–55CrossRefGoogle Scholar
  11. Gui J, Tao D, Sun Z et al (2014) Group sparse multiview patch alignment framework with view consistency for image classification. IEEE Trans Image Process 23(7):3126–3137MathSciNetCrossRefGoogle Scholar
  12. Hubert L, Arabie P (1985) Comparing partitions. J Classif 2(1):193–218CrossRefMATHGoogle Scholar
  13. Karasuyama M, Mamitsuka H (2013) Manifold-based similarity adaptation for label propagation. Adv Neural Inform Process Syst:1547–1555Google Scholar
  14. Kong D, Ding CHQ, Huang H et al (2012) An iterative locally linear embedding algorithm. arXiv preprint arXiv:1206.6463
  15. Kumar A, Rai P, Daume H (2011) Co-regularized multi-view spectral clustering. Adv Neural Inform Process Syst 2011:1413–1421Google Scholar
  16. Kumar A, Daum H (2011) A co-training approach for multi-view spectral clustering. Proceedings of the 28th International Conference on Machine Learning (ICML-11), pp 393–400Google Scholar
  17. Lee DD, Seung HS (2001) Algorithms for non-negative matrix factorization. Adv Neural Inform Process Syst:556–562Google Scholar
  18. Liu J, Wang C, Gao J et al (2013) Multi-view clustering via joint nonnegative matrix factorization. In: Proc. of SDM. vol 13, pp 252–260Google Scholar
  19. Long B, Philip SY, Zhongfei (Mark) Z (2008) A general model for multiple view unsupervised learning. SDM:822–833Google Scholar
  20. Lovsz L, Plummer MD (2009) Matching theory. In: American Mathematical SocietyGoogle Scholar
  21. Luo Y, Liu T, Tao D et al (2015) Multi-view matrix completion for multi-label image classification. IEEE Trans Image Process 24(8):2355–2368Google Scholar
  22. Manning CD, Raghavan P, Schtze H (2008) Introduction to information retrieval. Cambridge University Press, CambridgeCrossRefMATHGoogle Scholar
  23. Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500):2323–2326CrossRefGoogle Scholar
  24. Sun S (2013) A survey of multi-view machine learning. Neural Comput Appl 23(7–8):2031–2038CrossRefGoogle Scholar
  25. Sun S, Jin F (2011) Robust co-training. Int J Pattern Recogn Artif Intell 25(07):1113–1126MathSciNetCrossRefGoogle Scholar
  26. Tang W, Lu Z, Dhillon IS (2009) Clustering with multiple graphs, Data Mining. ICDM’09. Ninth IEEE International Conference on. IEEE, pp 1016–1021Google Scholar
  27. Tzortzis G, Likas A (2012) Kernel-based weighted multi-view clustering. Data Mining (ICDM), 2012 IEEE 12th International Conference on IEEE, pp 675–684Google Scholar
  28. Tzortzis GF, Likas AC (2010) Multiple view clustering using a weighted combination of exemplar-based mixture models. IEEE Trans Neural Netw 21(12):1925–1938CrossRefGoogle Scholar
  29. Von Luxburg U (2007) A tutorial on spectral clustering. Stat Comput 17(4):395–416MathSciNetCrossRefGoogle Scholar
  30. Wang W, Zhou ZH (2007) Analyzing co-training style algorithms. Machine Learning: ECML. Springer, Berlin Heidelberg, pp 454–465Google Scholar
  31. Wang W, Zhou ZH (2010) A new analysis of co-training. In: Proceedings of the 27th International Conference on Machine Learning (ICML-10), pp 1135–1142Google Scholar
  32. Xia T, Tao D, Mei T et al (2010) Multiview spectral embedding. IEEE Trans Syst Man Cybern Part B: Cybern 40(6):1438–1446CrossRefGoogle Scholar
  33. Xia R, Pan Y, Du L et al (2014) Robust multi-view spectral clustering via low-rank and sparse decomposition. In: AAAI Conference on Artificial Intelligence, pp 2149–2155Google Scholar
  34. Xu C, Tao D, Xu C (2015a) Multi-view learning with incomplete views. IEEE Trans Image Process 24(12):5812–5824MathSciNetCrossRefGoogle Scholar
  35. Xu C, Tao D, Xu C (2015b) Multi-view intact space learning. IEEE Trans Pattern Anal Mach Intell 37(12):2531–2544CrossRefGoogle Scholar
  36. Xu W, Liu X, Gong Y (2003) Document clustering based on non-negative matrix factorization. In: Proceedings of the 26th annual international ACM SIGIR conference on Research and development in informaion retrieval. ACM, pp 267–273Google Scholar
  37. Xu C, Tao D, Xu C (2013) A survey on multi-view learning. arXiv preprint: arXiv:1304.5634
  38. Xu C, Tao D, Xu C (2015c) Multi-view self-paced learning for clustering. In: Proceedings of the 24th International Conference on Artificial Intelligence. AAAI Press, pp 3974–3980Google Scholar
  39. Zhang Q, Zhang L, Zhang L et al (2015) Ensemble manifold regularized sparse low-rank approximation for multiview feature embedding. Pattern Recogn 48(10):3102–3112CrossRefGoogle Scholar
  40. Zhang X, Zhao L, Zong L et al (2014) Multi-view clustering via multi-manifold regularized nonnegative matrix factorization. Data Mining (ICDM), 2014 IEEE International Conference on IEEE, pp 1103–1108Google Scholar
  41. Zhuang J, Wang J, HOI CH et al (2011) Unsupervised multiple kernel learning. J Mach Learn Res (JMLR) 20:129–144Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Innovation and Entrepreneurship of DUTDalian University of TechnologyDalianChina
  2. 2.Student of Electronic Information and Electrical EngineeringDalian University of Technology DalianChina
  3. 3.Faculty of Electronic Information and Electrical EngineeringDalian University of TechnologyDalianChina

Personalised recommendations