Mixed-Norm Regression for Visual Classification

  • Xiaofeng Zhu
  • Jilian Zhang
  • Shichao Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8346)


This paper addresses the problem of multi-class image classification by proposing a novel multi-view multi-sparsity kernel reconstruction (MMKR for short) model. Given images (including test images and training images) representing with multiple visual features, the MMKR first maps them into a high-dimensional space, e.g., a reproducing kernel Hilbert space (RKHS), where test images are then linearly reconstructed by some representative training images, rather than all of them. Furthermore a classification rule is proposed to classify test images. Experimental results on real datasets show the effectiveness of the proposed MMKR while comparing to state-of-the-art algorithms.


image classification multi-view classification sparse coding Structure sparsity Reproducing kernel Hilbert space 


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  1. 1.
    Blum, A., Mitchell, T.: Combining labeled and unlabeled data with co-training. In: Annual Conference on Computational Learning Theory, pp. 92–100 (1998)Google Scholar
  2. 2.
    Boureau, Y.-L., Roux, N.L., Bach, F., Ponce, J., LeCun, Y.: Ask the locals: multi-way local pooling for image recognition. In: International Conference on Computer Vision, pp. 2651–2658 (2011)Google Scholar
  3. 3.
    Chen, N., Zhu, J., Xing, E.: Predictive subspace learning for multi-view data: A large margin approach. In: Advances in Neural Information Processing Systems (NIPS), vol. 23 (2010)Google Scholar
  4. 4.
    Dhillon, P.S., Foster, D., Ungar, L.: Multi-view learning of word embeddings via cca. In: Neural Information Processing Systems, pp. 9–16 (2011)Google Scholar
  5. 5.
    Gao, S., Tsang, I.W.-H., Chia, L.-T.: Kernel sparse representation for image classification and face recognition. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part IV. LNCS, vol. 6314, pp. 1–14. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Geng, B., Tao, D., Xu, C.: Daml: Domain adaptation metric learning. IEEE Transactions on Image Processing (99), 1 (2010)Google Scholar
  7. 7.
    Hou, C., Nie, F., Yi, D., Wu, Y.: Feature selection via joint embedding learning and sparse regression. In: IJCAI, pp. 1324–1329 (2011)Google Scholar
  8. 8.
    Jenatton, R., Audibert, J.-Y., Bach, F.: Structured variable selection with sparsity-inducing norms. Journal of Machine Learning Research 12, 2777 (2011)MathSciNetGoogle Scholar
  9. 9.
    Kim, J., Monteiro, R., Park, H.: Group sparsity in nonnegative matrix factorization. In: SIAM International Conference on Data Mining (2012)Google Scholar
  10. 10.
    Kumar, A., DauméIII, H.: A co-training approach for multi-view spectral clustering. In: International Conference on Machine Learning, pp. 393–400 (2011)Google Scholar
  11. 11.
    Mairal, J., Bach, F., Ponce, J., Sapiro, G.: Online learning for matrix factorization and sparse coding. Journal of Machine Learning Research 11, 19–60 (2010)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Nie, F., Huang, H., Cai, X., Ding, C.: Efficient and robust feature selection via joint l2,1-norms minimization. In: Neural Information Processing Systems, pp. 1813–1821 (2010)Google Scholar
  13. 13.
    Nilsback, M.-E., Zisserman, A.: A visual vocabulary for flower classification. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1447–1454 (2006)Google Scholar
  14. 14.
    Owens, T., Saenko, K., Chakrabarti, A., Xiong, Y., Zickler, T., Darrell, T.: Learning object color models from multi-view constraints. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 169–176 (2011)Google Scholar
  15. 15.
    Quadrianto, N., Lampert, C.H.: Learning multi-view neighborhood preserving projections. In: International Conference on Machine Learning, pp. 425–432 (2011)Google Scholar
  16. 16.
    Rakotomamonjy, A., Bach, F.R., Canu, S., Grandvalet, Y.: Simplemkl. Journal of Machine Learning Research 9, 2491–2521 (2008)zbMATHMathSciNetGoogle Scholar
  17. 17.
    Tan, M., Wang, L., Tsang, I.W.: Learning sparse svm for feature selection on very high dimensional datasets. In: International Conference on Machine Learning, pp. 1047–1054 (2010)Google Scholar
  18. 18.
    Wang, H., Nie, F., Huang, H., Ding, C.: Feature selection via joint embedding learning and sparse regression. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pp. 3097–3012 (2013)Google Scholar
  19. 19.
    Wu, J., Rehg, J.M.: Centrist: A visual descriptor for scene categorization. IEEE Transactions on Pattern Analysis and Machine Intelligence 33(8), 1489–1501 (2011)CrossRefGoogle Scholar
  20. 20.
    Xia, T., Tao, D., Mei, T., Zhang, Y.: Multiview spectral embedding. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 40(6), 1438–1446 (2010)CrossRefGoogle Scholar
  21. 21.
    Yuan, X., Yan, S.: Visual classification with multi-task joint sparse representation. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 3493–3500 (2010)Google Scholar
  22. 22.
    Zhu, X., Huang, Z., Cui, J., Shen, H.T.: Video-to-shot tag propagation by graph sparse group lasso. IEEE Transactions on Multimedia 15(3), 633–646 (2013)CrossRefGoogle Scholar
  23. 23.
    Zhu, X., Huang, Z., Wu, X.: Multi-view visual classification via a mixed-norm regularizer. In: Pei, J., Tseng, V.S., Cao, L., Motoda, H., Xu, G. (eds.) PAKDD 2013, Part I. LNCS, vol. 7818, pp. 520–531. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  24. 24.
    Zhu, X., Huang, Z., Yang, Y., Shen, H.T., Xu, C., Luo, J.: Self-taught dimensionality reduction on the high-dimensional small-sized data. Pattern Recognition 46(1), 215–229 (2013)CrossRefzbMATHGoogle Scholar
  25. 25.
    Zhu, X., Shen, H.T., Huang, Z.: Video-to-shot tag allocation by weighted sparse group lasso. In: ACM Multimedia, pp. 1501–1504 (2011)Google Scholar
  26. 26.
    Zou, H., Hastie, T., Tibshirani, R.: Sparse principal component analysis. Journal of Computational and Graphical Statistics 15(2), 265–286 (2006)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Xiaofeng Zhu
    • 1
  • Jilian Zhang
    • 1
  • Shichao Zhang
    • 1
    • 2
  1. 1.College of CS & ITGuangxi Normal UniversityGuilinChina
  2. 2.The Centre for QCIS, Faculty of Engineering and Information TechnologyUniversity of Technology SydneyAustralia

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