Signal, Image and Video Processing

, Volume 13, Issue 7, pp 1387–1394 | Cite as

Classification via semi-supervised multi-random subspace sparse representation

  • Zhuang Zhao
  • Lianfa Bai
  • Yi Zhang
  • Jing HanEmail author
Original Paper


In this paper, we combine the random subspace and multi-view together and obtain a novel approach named semi-supervised multi-random subspace sparse representation (SSM-RSSR). In the proposed SSM-RSSR, firstly, we use subspace sparse representation to obtain the graph to characterize the distribution of samples in each subspace. Then, we fuse these graphs in the viewpoint of multi-view through an alternating optimization method and obtain the optimal coefficients of all random subspaces. Finally, we train a linear classifier under the framework of manifold regularization (MR) to obtain the final classified results. Through fusing the random subspaces, the proposed SSM-RSSR can obtain better and more stable results in a wider range of the dimension of random subspace and the number of random subspaces. Extensive experimental results on the several UCI datasets and face image datasets have demonstrated the effectiveness of the proposed SSM-RSSR.


Semi-supervised classification Sparse representation Random subspace Multi-view 



This work is supported by the National Natural Science Foundation of China (Grant No. 61727802, 61601225).


  1. 1.
    Belhumeur, P.N., Hespanha, J.P., Kriegman, D.J.: Eigenfaces vs fisherfaces: recognition using class specific linear projection. IEEE Trans. Pattern Anal. Mach. Intell. 19(7), 711–720 (1997)CrossRefGoogle Scholar
  2. 2.
    Li, B., Huang, D.S., Wang, C., Liu, K.H.: Feature extraction using constrained maximum variance mapping. Pattern Recognit. 41(11), 3287–3294 (2008)CrossRefGoogle Scholar
  3. 3.
    Yang, W.K., Sun, C.Y., Zhang, L.: A multi-manifold discriminant analysis method for image feature extraction. Pattern Recognit. 44(8), 1649–1657 (2011)CrossRefGoogle Scholar
  4. 4.
    Wold, S., Esbensen, K., Geladi, P.: Principal component analysis. Chemom. Intell. Lab. Syst. 2(1), 37–52 (1987)CrossRefGoogle Scholar
  5. 5.
    Tenenbaum, J.B., Silva, V.D., Langform, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5000), 2319–2323 (2000)CrossRefGoogle Scholar
  6. 6.
    Roweis, S.T., Saul, L.K.: Nonlinear dimension reduction by locally linear embedding. Science 290(5), 2323–2326 (2000)CrossRefGoogle Scholar
  7. 7.
    Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neurocomputing 15(6), 1373–1396 (2003)zbMATHGoogle Scholar
  8. 8.
    He, X.F., Yan, S.C., Hu, Y.X., Niuogi, P., Zhang, H.J.: Face recognition using laplacian faces. IEEE Trans. Pattern Anal. Mach. Intell. 27(3), 328–340 (2005)CrossRefGoogle Scholar
  9. 9.
    Ramirez, I., Sprechmann, P., Sapiro, G.: Classification and clustering via dictionary learning with structured incoherence and shared features. In: IEEE conference on computer vision and pattern recognition, pp. 3501–3508 (2010)Google Scholar
  10. 10.
    Ho, T.K.: The random subspace method for constructing decision forests. IEEE Trans. Pattern Anal. Mach. Intell. 20(8), 832–844 (1998)CrossRefGoogle Scholar
  11. 11.
    Yu, G.X., Zhang, G., Domeniconi, C., Yu, Z.W., You, J.: Semi-supervised classification based on random subspace dimensionality reduction. Pattern Recognit. 45(3), 1119–1135 (2012)CrossRefGoogle Scholar
  12. 12.
    Yu, G.X., Zhang, G., Yu, Z.W., Domeniconi, C., You, J., Han, G.Q.: Semi-supervised ensemble classification in subspaces. Appl. Soft Comput. 12(5), 1511–1522 (2012)CrossRefGoogle Scholar
  13. 13.
    Yu, G.X., Zhang, G.J., Zhang, Z.L., Yu, Z.W., Lin, D.: Semi-supervised classification based on subspace sparse representation. Knowl. Inf. Syst. 43(1), 81–101 (2015)CrossRefGoogle Scholar
  14. 14.
    Zhao, Z., Bai, L.F., Zhang, Y., Han, J.: Probabilistic semi-supervised random subspace sparse representation for classification. Multimed. Tools Appl. 77(18), 23245–23271 (2018)CrossRefGoogle Scholar
  15. 15.
    Zhu, X.J., Ghahramani, Z.B., Lafferty, J.: Semi-supervised learning using gaussian fields and harmonic functions. In: International Conference on Machine Learning, pp. 912–919 (2003)Google Scholar
  16. 16.
    Cai, D., He, X.F., Han, J.W.: Semi-supervised discriminant analysis. In: IEEE International Conference on Computer Vision, pp. 1–7 (2007)Google Scholar
  17. 17.
    Belkin, M., Niyogi, P., Sindhwani, V.: Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. J. Mach. Learn. Res. 7, 2399–2434 (2006)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Wu, F., Wang, W.H., Yang, Y., Zhuang, Y.T., Nie, F.P.: Classification by semi-supervised discriminative regularization. Neurocomputing 73(10), 1641–1651 (2010)CrossRefGoogle Scholar
  19. 19.
    Fan, M.Y., Gu, N., Qiao, H., Zhang, B.: Sparse regularization for semi-supervised classification. Pattern Recognit. 44(8), 1777–1784 (2011)CrossRefGoogle Scholar
  20. 20.
    Zhao, M.B., Zhan, C., Wu, Z., Tang, P.: Semi-supervised image classification based on local and global regression. IEEE Signal Process. Lett. 22(10), 1666–1670 (2015)CrossRefGoogle Scholar
  21. 21.
    Figueiredo, M.A.T., Nowak, R.D., Wright, S.J.: Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007)CrossRefGoogle Scholar
  22. 22.
    Jenatton, R., Mairal, J., Obozinski, G., Bach, F.: Proximal methods for sparse hierarchical dictionary learning. In: International Conference on Machine Learning, pp. 487–494 (2010)Google Scholar
  23. 23.
    Bezdek, J.C., Hathaway, R.J.: Some notes on alternating optimization. In: AFSS International Conference on Fuzzy Systems (Springer, Berlin, 2002), pp. 288–300CrossRefGoogle Scholar
  24. 24.
    Cevikalp, H., Verbeek, J., Jurie, F., Klaser, A.: Semi-supervised dimensionality reduction using pairwise equivalence constraints. Conf. Comput. Vision Imaging Comput. Graph. Theory Appl. 1, 489–496 (2008)Google Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Jiangsu Key Laboratory of Spectral Imaging and Intelligent SenseNanjing University of Science and TechnologyNanjingChina

Personalised recommendations