Self-Paced Multi-Task Multi-View Capped-norm Clustering

  • Yazhou RenEmail author
  • Xin Yan
  • Zechuan Hu
  • Zenglin Xu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11304)


Recently, multi-task multi-view clustering (MTMVC) which is able to utilize the relation of different tasks and the information from multiple views under each task to improve the clustering performance has attracted more and more attentions. However, MTMVC typically solves a non-convex optimization problem and thus is easy to stuck into bad local optima. In addition, noises and outliers generally have negative effects on the clustering performance. To alleviate these problems, we propose a novel self-paced multi-task multi-view capped-norm clustering (SPMTMVCaC) method, which progressively selects data samples to train the MTMVC model from simplicity to complexity. A novel capped-norm term is embedded into the objective of SPMTMVCaC model to reduce the negative influence of noises and outliers, and to further enhance the clustering performance. An efficient alternating optimization method is developed to solve the proposed model. Experimental results on real data sets demonstrate the effectiveness and robustness of the proposed method.


Multi-Task Muti-View Clustering Self-paced learning Capped-norm 



This paper was in part supported by Grants from the Natural Science Foundation of China (Nos. 61806043, 61572111, and 61872062), a Project funded by China Postdoctoral Science Foundation (No. 2016M602674), a 985 Project of UESTC (No. A1098531023601041), and two Fundamental Research Funds for the Central Universities of China (Nos. ZYGX2016J078 and ZYGX2016Z003).


  1. 1.
    Ankerst, M., Breunig, M.M., Kriegel, H.P., Sander, J.: OPTICS: ordering points to identify the clustering structure. In: SIGMOD, pp. 49–60 (1999)Google Scholar
  2. 2.
    Comaniciu, D., Meer, P.: Mean shift: a robust approach toward feature space analysis. PAMI 24(5), 603–619 (2002)CrossRefGoogle Scholar
  3. 3.
    Dhillon, I.S.: Co-clustering documents and words using bipartite spectral graph partitioning. In: SIGKDD, pp. 269–274 (2001)Google Scholar
  4. 4.
    Dhillon, I.S., Guan, Y., Kulis, B.: Kernel k-means: spectral clustering and normalized cuts. In: SIGKDD, pp. 551–556 (2004)Google Scholar
  5. 5.
    Ester, M., Kriegel, H.P., Sander, J., Xu, X.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: SIGKDD, pp. 226–231 (1996)Google Scholar
  6. 6.
    Evgeniou, T., Pontil, M.: regularized multi-task learning. In: SIGKDD, pp. 109–117. ACM (2004)Google Scholar
  7. 7.
    Gao, H., Nie, F., Cai, W., Huang, H.: Robust capped norm nonnegative matrix factorization: capped norm NMF. In: CIKM, pp. 871–880 (2015)Google Scholar
  8. 8.
    Gu, Q., Zhou, J.: Learning the shared subspace for multi-task clustering and transductive transfer classification. In: ICDM, pp. 159–168 (2009)Google Scholar
  9. 9.
    Huang, S., Kang, Z., Xu, Z.: Self-weighted multi-view clustering with soft capped norm. Knowl. Based Syst. 158, 1–8 (2018)CrossRefGoogle Scholar
  10. 10.
    Huang, S., Ren, Y., Xu, Z.: Robust multi-view data clustering with multi-view capped-norm k-means. Neurocomputing 311, 197–208 (2018)CrossRefGoogle Scholar
  11. 11.
    Huang, S., Wang, H., Li, T., Li, T., Xu, Z.: Robust graph regularized nonnegative matrix factorization for clustering. Data Min. Knowl. Discov. 32(2), 483–503 (2018)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Huang, S., Xu, Z., Lv, J.: Adaptive local structure learning for document co-clustering. Knowl. Based Syst. 148, 74–84 (2018)CrossRefGoogle Scholar
  13. 13.
    Jiang, L., Meng, D., Mitamura, T., Hauptmann, A.G.: Easy samples first: self-paced reranking for zero-example multimedia search. In: ACM MM, pp. 547–556 (2014)Google Scholar
  14. 14.
    Jiang, L., Meng, D., Zhao, Q., Shan, S., Hauptmann, A.G.: Self-paced curriculum learning. In: AAAI, pp. 2694–2700 (2015)Google Scholar
  15. 15.
    Kang, Z., Lu, X., Yi, J., Xu, Z.: Self-weighted multiple kernel learning for graph-based clustering and semi-supervised classification. In: IJCAI, pp. 2312–2318 (2018)Google Scholar
  16. 16.
    Kang, Z., Peng, C., Cheng, Q., Xu, Z.: Unified spectral clustering with optimal graph. In: AAAI (2018)Google Scholar
  17. 17.
    Kaufman, L., Rousseeuw, P.: Clustering by means of medoids. Faculty of Mathematics and Informatics (1987).
  18. 18.
    Kim, H.K., Kim, H., Cho, S.: Bag-of-concepts: comprehending document representation through clustering words in distributed representation. Neurocomputing 266, 336–352 (2017)CrossRefGoogle Scholar
  19. 19.
    Kumar, A., Rai, P.: Co-regularized multi-view spectral clustering. In: ICONIP, pp. 1413–1421 (2011)Google Scholar
  20. 20.
    Kumar, M.P., Packer, B., Koller, D.: Self-paced learning for latent variable models. In: NIPS, pp. 1189–1197 (2010)Google Scholar
  21. 21.
    Liu, B., et al.: Learning from semantically dependent multi-tasks. In: IJCNN, pp. 3498–3505 (2017)Google Scholar
  22. 22.
    MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–297 (1967)Google Scholar
  23. 23.
    Pi, T., et al.: Self-paced boost learning for classification. In: IJCAI, pp. 1932–1938 (2016)Google Scholar
  24. 24.
    Que, X., Ren, Y., Zhou, J., Xu, Z.: Regularized multi-source matrix factorization for diagnosis of Alzheimer’s disease. In: Liu, D., Xie, S., Li, Y., Zhao, D., El-Alfy, E.S. (eds.) Neural Information Processing. ICONIP 2017. LNCS, vol. 10634, pp. 463–473. Springer, Cham (2017). Scholar
  25. 25.
    Ren, Y.: Big data clustering and its applications in regional science. In: Schintler, L.A., Chen, Z. (eds.) Big Data for Regional Science, pp. 257–264. Routledge, London (2018). chap. 21Google Scholar
  26. 26.
    Ren, Y., Domeniconi, C., Zhang, G., Yu, G.: Weighted-object ensemble clustering. In: ICDM, pp. 627–636 (2013)Google Scholar
  27. 27.
    Ren, Y., Domeniconi, C., Zhang, G., Yu, G.: A weighted adaptive mean shift clustering algorithm. In: SDM, pp. 794–802 (2014)Google Scholar
  28. 28.
    Ren, Y., Domeniconi, C., Zhang, G., Yu, G.: Weighted-object ensemble clustering: methods and analysis. KAIS 51(2), 661–689 (2017)Google Scholar
  29. 29.
    Ren, Y., Hu, X., Shi, K., Yu, G., Yao, D., Xu, Z.: Semi-supervised DenPeak clustering with pairwise constraints. In: Geng, X., Kang, B.-H. (eds.) PRICAI 2018. LNCS (LNAI), vol. 11012, pp. 837–850. Springer, Cham (2018). Scholar
  30. 30.
    Ren, Y., Kamath, U., Domeniconi, C., Zhang, G.: Boosted mean shift clustering. In: Calders, T., Esposito, F., Hüllermeier, E., Meo, R. (eds.) ECML PKDD 2014. LNCS (LNAI), vol. 8725, pp. 646–661. Springer, Heidelberg (2014). Scholar
  31. 31.
    Ren, Y., Que, X., Yao, D., Xu, Z.: Self-paced multi-task clustering. arXiv preprint arXiv:1808.08068 (2018)
  32. 32.
    Ren, Y., Zhao, P., Sheng, Y., Yao, D., Xu, Z.: Robust softmax regression for multi-class classification with self-paced learning. In: IJCAI, pp. 2641–2647 (2017)Google Scholar
  33. 33.
    Ren, Y., Zhao, P., Xu, Z., Yao, D.: Balanced self-paced learning with feature corruption. In: IJCNN, pp. 2064–2071 (2017)Google Scholar
  34. 34.
    Strehl, A., Ghosh, J.: Cluster ensembles - a knowledge reuse framework for combining multiple partitions. JMLR 3, 583–617 (2002)MathSciNetzbMATHGoogle Scholar
  35. 35.
    Tang, K., Ramanathan, V., Li, F.F., Koller, D.: Shifting weights: adapting object detectors from image to video. In: NIPS, pp. 647–655 (2012)Google Scholar
  36. 36.
    Wang, H., Nie, F., Huang, H., Makedon, F.: Fast nonnegative matrix tri-factorization for large-scale data co-clustering. In: IJCAI, pp. 1553–1558 (2011)Google Scholar
  37. 37.
    Xie, P., Xing, E.P.: Integrating image clustering and codebook learning. In: AAAI, pp. 1903–1909 (2015)Google Scholar
  38. 38.
    Zhang, X., Zhang, X., Liu, H.: Multi-task multi-view clustering for non-negative data. In: IJCAI, pp. 4055–4061 (2015)Google Scholar
  39. 39.
    Zhang, X., Zhang, X., Liu, H., Liu, X.: Multi-task multi-view clustering. TKDE 28(12), 3324–3338 (2016)Google Scholar
  40. 40.
    Zhu, H., Pan, X., Xie, Q.: Merging students-t and Rayleigh distributions regression mixture model for clustering time-series. Neurocomputing 266, 247–262 (2017)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.SMILE Lab, School of Computer Science and EngineeringUniversity of Electronic Science and Technology of ChinaChengduChina

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