Advertisement

Multiple Incomplete Views Clustering via Weighted Nonnegative Matrix Factorization with \(L_{2,1}\) Regularization

  • Weixiang Shao
  • Lifang HeEmail author
  • Philip S. Yu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9284)

Abstract

With the advance of technology, data are often with multiple modalities or coming from multiple sources. Multi-view clustering provides a natural way for generating clusters from such data. Although multi-view clustering has been successfully applied in many applications, most of the previous methods assumed the completeness of each view (i.e., each instance appears in all views). However, in real-world applications, it is often the case that a number of views are available for learning but none of them is complete. The incompleteness of all the views and the number of available views make it difficult to integrate all the incomplete views and get a better clustering solution. In this paper, we propose MIC (Multi-Incomplete-view Clustering), an algorithm based on weighted nonnegative matrix factorization with \( L_{2,1} \) regularization. The proposed MIC works by learning the latent feature matrices for all the views and generating a consensus matrix so that the difference between each view and the consensus is minimized. MIC has several advantages comparing with other existing methods. First, MIC incorporates weighted nonnegative matrix factorization, which handles the missing instances in each incomplete view. Second, MIC uses a co-regularized approach, which pushes the learned latent feature matrices of all the views towards a common consensus. By regularizing the disagreement between the latent feature matrices and the consensus, MIC can be easily extended to more than two incomplete views. Third, MIC incorporates \( L_{2,1} \) regularization into the weighted nonnegative matrix factorization, which makes it robust to noises and outliers. Forth, an iterative optimization framework is used in MIC, which is scalable and proved to converge. Experiments on real datasets demonstrate the advantages of MIC.

Keywords

Normalize Mutual Information Nonnegative Matrix Factorization Credit Score Common Consensus Consensus Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bickel, S., Scheffer, T.: Multi-view clustering. In: ICDM, pp. 19–26 (2004)Google Scholar
  2. 2.
    Blum, A., Mitchell, T.: Combining labeled and unlabeled data with co-training. In: COLT, New York, NY, USA, pp. 92–100 (1998)Google Scholar
  3. 3.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, New York (2004)CrossRefzbMATHGoogle Scholar
  4. 4.
    Bruno, E., Marchand-Maillet, S.: Multiview clustering: a late fusion approach using latent models. In: SIGIR. ACM, New York (2009)Google Scholar
  5. 5.
    Chaudhuri, K., Kakade, S.M., Livescu, K., Sridharan, K.: Multi-view clustering via canonical correlation analysis. In: ICML, New York, NY, USA (2009)Google Scholar
  6. 6.
    Cheng, W., Zhang, X., Guo, Z., Wu, Y., Sullivan, P.F., Wang, W.: Flexible and robust co-regularized multi-domain graph clustering. In: SIGKDD, pp. 320–328. ACM (2013)Google Scholar
  7. 7.
    de Sa, V.R.: Spectral clustering with two views. In: ICML Workshop on Learning with Multiple Views (2005)Google Scholar
  8. 8.
    Ding, C., Li, T., Peng, W., Park, H.: Orthogonal nonnegative matrix T-factorizations for clustering. In: SIGKDD, pp. 126–135. ACM (2006)Google Scholar
  9. 9.
    Ding, C., Zhou, D., He, X., Zha, H.: R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization. In: ICML, pp. 281–288. ACM (2006)Google Scholar
  10. 10.
    Ding, W., Wu, X., Zhang, S., Zhu, X.: Feature selection by joint graph sparse coding. In: SDM, Austin, Texas, pp. 803–811, May 2013Google Scholar
  11. 11.
    L. Du, X. Li, and Y. Shen. Robust nonnegative matrix factorization via half-quadratic minimization. In: ICDM, pp. 201–210 (2012)Google Scholar
  12. 12.
    Duin, R.P.: Handwritten-Numerals-DatasetGoogle Scholar
  13. 13.
    Evgeniou, A., Pontil, M.: Multi-task Feature Learning. Advances in Neural Information Processing Systems 19, 41 (2007)Google Scholar
  14. 14.
    Févotte, C.: Majorization-minimization algorithm for smooth itakura-saito nonnegative matrix factorization. In: ICASSP, pp. 1980–1983. IEEE (2011)Google Scholar
  15. 15.
    Greene, D., Cunningham, P.: A matrix factorization approach for integrating multiple data views. In: Buntine, W., Grobelnik, M., Mladenić, D., Shawe-Taylor, J. (eds.) ECML PKDD 2009, Part I. LNCS, vol. 5781, pp. 423–438. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  16. 16.
    Gu, Q., Zhou, J., Ding, C.: Collaborative filtering: weighted nonnegative matrix factorization incorporating user and item graphs. In: SDM. SIAM (2010)Google Scholar
  17. 17.
    Guo, Y.: Convex subspace representation learning from multi-view data. In: AAAI, Bellevue, Washington, USA (2013)Google Scholar
  18. 18.
    Huang, H., Ding, C.: Robust tensor factorization using R1 norm. In: CVPR, pp. 1–8. IEEE (2008)Google Scholar
  19. 19.
    Kim, J., Park, H.: Sparse Nonnegative Matrix Factorization for Clustering (2008)Google Scholar
  20. 20.
    Kim, Y., Choi, S.: Weighted nonnegative matrix factorization. In: International Conference on Acoustics, Speech and Signal Processing, pp. 1541–1544 (2009)Google Scholar
  21. 21.
    Kong, D., Ding, C., Huang, H.: Robust nonnegative matrix factorization using L21-norm. In: CIKM, New York, NY, USA, pp. 673–682 (2011)Google Scholar
  22. 22.
    Kriegel, H.P., Kunath, P., Pryakhin, A., Schubert, M.: MUSE: multi-represented similarity estimation. In: ICDE, pp. 1340–1342 (2008)Google Scholar
  23. 23.
    Kumar, A., Daume III, H.: A co-training approach for multi-view spectral clustering. In: ICML, New York, NY, USA, pp. 393–400, June 2011Google Scholar
  24. 24.
    Kumar, A., Rai, P., Daumé III, H.: Co-regularized multi-view spectral clustering. In: NIPS, pp. 1413–1421 (2011)Google Scholar
  25. 25.
    Lee, D., Seung, S.: Learning the Parts of Objects by Nonnegative Matrix Factorization. Nature 401, 788–791 (1999)CrossRefGoogle Scholar
  26. 26.
    Li, S., Jiang, Y., Zhou, Z.: Partial multi-view clustering. In: AAAI, pp. 1968–1974 (2014)Google Scholar
  27. 27.
    Liu, J., Wang, C., Gao, J., Han, J.: Multi-view clustering via joint nonnegative matrix factorization. In: SDM (2013)Google Scholar
  28. 28.
    Long, B., Philip, S.Y., (Mark) Zhang, Z.: A general model for multiple view unsupervised learning. In: SDM, pp. 822–833. SIAM (2008)Google Scholar
  29. 29.
    Nigam, K., Ghani, R.: Analyzing the effectiveness and applicability of co-training. In CIKM, pp. 86–93. ACM, New York (2000)Google Scholar
  30. 30.
    Nilsback, M.-E., Zisserman, A.: A visual vocabulary for flower classification. In: CVPR, vol. 2, pp. 1447–1454 (2006)Google Scholar
  31. 31.
    Shahnaz, F., Berry, M., Pauca, V.P., Plemmons, R.: Document Clustering Using Nonnegative Matrix Factorization. Information Processing & Management 42(2), 373–386 (2006)CrossRefzbMATHGoogle Scholar
  32. 32.
    Shao, W., Shi, X., Yu, P.: Clustering on multiple incomplete datasets via collective kernel learning. In: ICDM (2013)Google Scholar
  33. 33.
    Tang, W., Lu, Z., Dhillon, I.S.: Clustering with multiple graphs. In: ICDM, Miami, Florida, USA, pp. 1016–1021, December 2009Google Scholar
  34. 34.
    Trivedi, A., Rai, P., Daumé III, H., DuVall, S.L.: Multiview clustering with incomplete views. In: NIPS 2010: Workshop on Machine Learning for Social Computing, Whistler, Canada (2010)Google Scholar
  35. 35.
    Wang, D., Li, T., Ding, C.: Weighted feature subset non-negative matrix factorization and its applications to document understanding. In: ICDM (2010)Google Scholar
  36. 36.
    Xu, W., Liu, X., Gong, Y.: Document clustering based on non-negative matrix factorization. In: SIGIR, pp. 267–273 (2003)Google Scholar
  37. 37.
    Zhang, X., Yu, Y., White, M., Huang, R., Schuurmans, D.: Convex sparse coding, subspace learning, and semi-supervised extensions. In: AAAI (2011)Google Scholar
  38. 38.
    Zhou, D., Burges, C.: Spectral clustering and transductive learning with multiple views. In: ICML, pp. 1159–1166. ACM, New York (2007)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Illinois at ChicagoChicagoUSA
  2. 2.Institute for Computer VisionShenzhen UniversityShenzhenChina
  3. 3.Institute for Data ScienceTsinghua UniversityBeijingChina

Personalised recommendations