Face Subspace Learning


In this chapter, we will present three groups of dimension reduction algorithms for subspace based face recognition. Specifically, we present the general mean criteria and the max-min distance analysis (MMDA) algorithm; manifold learning algorithms, including the discriminative locality alignment (DLA) and manifold elastic net (MEN); and the transfer subspace learning framework. Experiments on face recognition are also provided.


  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.
    Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6), 1373–1396 (2003) MATHCrossRefGoogle Scholar
  3. 3.
    Bian, W., Tao, D.: Harmonic mean for subspace selection. In: 19th International Conference on Pattern Recognition, pp. 1–4 (2008) CrossRefGoogle Scholar
  4. 4.
    Bian, W., Tao, D.: Manifold regularization for sir with rate root-n convergence (2010) Google Scholar
  5. 5.
    Bian, W., Tao, D.: Max-min distance analysis by using sequential sdp relaxation for dimension reduction. IEEE Trans. Pattern Anal. Mach. Intell. 99(PrePrints) (2010) Google Scholar
  6. 6.
    Bishop, C.M., Svensén, M., Williams, C.K.I.: GTM: The generative topographic mapping. Technical Report NCRG/96/015, Neural Computing Research Group, Dept of Computer Science & Applied Mathematics, Aston University, Birmingham B4 7ET, United Kingdom, April 1997 Google Scholar
  7. 7.
    Cai, D., He, X., Han, J.: Using graph model for face analysis. Technical report, Computer Science Department, UIUC, UIUCDCS-R-2005-2636, September 2005 Google Scholar
  8. 8.
    Cai, D., He, X., Han, J.: Srda: An efficient algorithm for large-scale discriminant analysis. IEEE Trans. Knowl. Data Eng. 20(1), 1–12 (2008) CrossRefGoogle Scholar
  9. 9.
    D’aspremont, A., Ghaoui, L.E., Jordan, M.I., Lanckriet, G.R.G.: A direct formulation for sparse PCA using semidefinite programming. SIAM Rev. 49(3), 434–448 (2007) MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Decell, H., Mayekar, S.: Feature combinations and the divergence criterion. Comput. Math. Appl. 3(4), 71–76 (1977) MATHCrossRefGoogle Scholar
  11. 11.
    Donoho, D.L., Grimes, C.: Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. Proc. Natl. Acad. Sci. USA 100(10), 5591–5596 (2003) MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Edelman, A., Arias, T.A., Smith, S.T.: The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 20, 303–353 (1998) MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Efron, B., Hastie, T., Johnstone, L., Tibshirani, R.: Least angle regression. Ann. Stat. 32, 407–499 (2004) MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Fisher, R.A.: The use of multiple measurements in taxonomic problems. Ann. Eugen. 7, 179–188 (1936) CrossRefGoogle Scholar
  15. 15.
    Fukunaga, K.: Introduction to Statistical Pattern Recognition, 2nd edn. Academic Press, San Diego (1990) MATHGoogle Scholar
  16. 16.
    Fukunaga, K., Mantock, J.: Nonparametric discriminant analysis. IEEE Trans. Pattern Anal. Mach. Intell. 5, 671–678 (1983) MATHCrossRefGoogle Scholar
  17. 17.
    Graham, D.B., Allinson, N.M.: Characterizing virtual eigensignatures for general purpose face recognition. In: Wechsler, H., Phillips, P.J., Bruce, V., Fogelman-Soulie, F., Huang, T.S. (eds.) Face Recognition: From Theory to Applications. NATO ASI Series F, Computer and Systems Sciences, vol. 163, pp. 446–456 (1998) Google Scholar
  18. 18.
    Hamsici, O.C., Martinez, A.M.: Bayes optimality in linear discriminant analysis. IEEE Trans. Pattern Anal. Mach. Intell. 30(4), 647–657 (2008) CrossRefGoogle Scholar
  19. 19.
    He, X., Cai, D., Yan, S., Zhang, H.-J.: Neighborhood preserving embedding. In: Proc. Int. Conf. Computer Vision (ICCV’05) (2005) Google Scholar
  20. 20.
    He, X., Niyogi, P.: Locality preserving projections. In: Thrun, S., Saul, L., Scholkopf, B. (eds.) Advances in Neural Information Processing Systems, vol. 16. MIT Press, Cambridge (2004) Google Scholar
  21. 21.
    He, X., Yan, S., Hu, Y., Niyogi, P.: Face recognition using Laplacianfaces. IEEE Trans. Pattern Anal. Mach. Intell. 27(3), 328–340 (2005) CrossRefGoogle Scholar
  22. 22.
    Huang, J., Smola, A.J., Gretton, A., Borgwardt, K.M., Schölkopf, B.: Correcting sample selection bias by unlabeled data. In: NIPS, pp. 601–608 (2006) Google Scholar
  23. 23.
    Jolliffe, I.: Principal Component Analysis, 2nd edn. Springer Series in Statistics, Springer, New York (2002) MATHGoogle Scholar
  24. 24.
    Li, L.: Sparse sufficient dimension reduction. Biometrika 94(3), 603–613 (2007) MathSciNetMATHCrossRefGoogle Scholar
  25. 25.
    Li, S.Z.: Face recognition based on nearest linear combinations. In: CVPR, pp. 839–844 (1998) Google Scholar
  26. 26.
    Li, S.Z., Lu, J.: Face recognition using the nearest feature line method. IEEE Trans. Neural Netw. 10(2), 439–443 (1999) CrossRefGoogle Scholar
  27. 27.
    Li, Z., Lin, D., Tang, X.: Nonparametric discriminant analysis for face recognition. IEEE Trans. Pattern Anal. Mach. Intell. 31(4), 755–761 (2009) CrossRefGoogle Scholar
  28. 28.
    Loog, M., Duin, R., Haeb-Umbach, R.: Multiclass linear dimension reduction by weighted pairwise Fisher criteria. IEEE Trans. Pattern Anal. Mach. Intell. 23(7), 762–766 (2001) CrossRefGoogle Scholar
  29. 29.
    Loog, M., Duin, R.P.W.: Linear dimensionality reduction via a heteroscedastic extension of lda: The Chernoff criterion. IEEE Trans. Pattern Anal. Mach. Intell. 26, 732–739 (2004) CrossRefGoogle Scholar
  30. 30.
    Lotlikar, R., Kothari, R.: Fractional-step dimensionality reduction. IEEE Trans. Pattern Anal. Mach. Intell. 22(6), 623–627 (2000) CrossRefGoogle Scholar
  31. 31.
    Pan, S.J., Kwok, J.T., Yang, Q.: Transfer learning via dimensionality reduction. In: Proc. of the Twenty-Third AAAI Conference on Artificial Intelligence (2008) Google Scholar
  32. 32.
    Phillips, P.J., Moon, H., Rizvi, S.A., Rauss, P.J.: The Feret evaluation methodology for face-recognition algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 22, 1090–1104 (2000) CrossRefGoogle Scholar
  33. 33.
    Rao, C.R.: The utilization of multiple measurements in problems of biological classification. J. R. Stat. Soc., Ser. B, Methodol. 10(2), 159–203 (1948) MATHGoogle Scholar
  34. 34.
    Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000) CrossRefGoogle Scholar
  35. 35.
    Saon, G., Padmanabhan, M.: Minimum Bayes error feature selection for continuous speech recognition. In: Advances in Neural Information Processing Systems, vol. 13, pp. 800–806. MIT Press, Cambridge (2001) Google Scholar
  36. 36.
    Schervish, M.: Linear discrimination for three known normal populations. J. Stat. Plan. Inference 10, 167–175 (1984) MathSciNetMATHCrossRefGoogle Scholar
  37. 37.
    Shakhnarovich, G., Moghaddam, B.: Face recognition in subspaces. In: Handbook of Face Recognition, pp. 141–168 (2004) Google Scholar
  38. 38.
    Si, S., Tao, D., Geng, B.: Bregman divergence-based regularization for transfer subspace learning. IEEE Trans. Knowl. Data Eng. 22(7), 929–942 (2010) CrossRefGoogle Scholar
  39. 39.
    Tao, D., Li, X., Wu, X., Maybank, S.J.: Geometric mean for subspace selection. IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 260–274 (2009) CrossRefGoogle Scholar
  40. 40.
    Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000) CrossRefGoogle Scholar
  41. 41.
    Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc., Ser. B, Stat. Methodol. 58, 267–288 (1996) MathSciNetMATHGoogle Scholar
  42. 42.
    Tipping, M.E., Bishop, C.M.: Probabilistic principal component analysis. J. R. Stat. Soc., Ser. B, Stat. Methodol. 61(3), 611–622 (1999) MathSciNetMATHCrossRefGoogle Scholar
  43. 43.
    Turk, M., Pentland, A.: Eigenfaces for recognition. J. Cogn. Neurosci. 3, 71–86 (1991) CrossRefGoogle Scholar
  44. 44.
    Wang, X., Tang, X.: A unified framework for subspace face recognition. IEEE Trans. Pattern Anal. Mach. Intell. 26, 1222–1228 (2004) CrossRefGoogle Scholar
  45. 45.
    Wang, X., Tang, X.: Subspace analysis using random mixture models. In: Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), vol. 1, pp. 574–580 (2005) CrossRefGoogle Scholar
  46. 46.
    Wang, X., Tang, X.: Random sampling for subspace face recognition. Int. J. Comput. Vis. 70, 91–104 (2006) CrossRefGoogle Scholar
  47. 47.
    Wright, J., Yang, A.Y., Ganesh, A., Sastry, S.S., Ma, Y.: Robust face recognition via sparse representation. IEEE Trans. Pattern Anal. Mach. Intell. 31, 210–227 (2009) CrossRefGoogle Scholar
  48. 48.
    Yan, S., Xu, D., Zhang, B., Zhang, H.-J., Yang, Q., Lin, S.: Graph embedding and extensions: A general framework for dimensionality reduction. IEEE Trans. Pattern Anal. Mach. Intell. 29(1), 40–51 (2007) CrossRefGoogle Scholar
  49. 49.
    Ye, J.: Least squares linear discriminant analysis. In: Proceedings of the 24th International Conference on Machine Learning, ICML ’07, pp. 1087–1093 (2007) CrossRefGoogle Scholar
  50. 50.
    Ye, J., Ji, S.: Discriminant analysis for dimensionality reduction: An overview of recent developments. In: Boulgouris, N., Plataniotis, K.N., Micheli-Tzanakou, E. (eds.) Biometrics: Theory, Methods, and Applications. Wiley-IEEE Press, New York (2010). Chap. 1 Google Scholar
  51. 51.
    Ye, J., Li, Q.: A two-stage linear discriminant analysis via qr-decomposition. IEEE Trans. Pattern Anal. Mach. Intell. 27(6), 929–941 (2005) CrossRefGoogle Scholar
  52. 52.
    Ye, J., Li, Q.: A two-stage linear discriminant analysis via qr-decomposition. IEEE Trans. Pattern Anal. Mach. Intell. 27, 929–941 (2005) CrossRefGoogle Scholar
  53. 53.
    Zhang, Z., Zha, H.: Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM J. Sci. Comput. 26, 313–338 (2005) MathSciNetCrossRefGoogle Scholar
  54. 54.
    Zhang, T., Tao, D., Yang, J.: Discriminative locality alignment. In: Proceedings of the 10th European Conference on Computer Vision, pp. 725–738, Berlin, Heidelberg, 2008 Google Scholar
  55. 55.
    Zhang, T., Tao, D., Li, X., Yang, J.: Patch alignment for dimensionality reduction. IEEE Trans. Knowl. Data Eng. 21, 1299–1313 (2009) CrossRefGoogle Scholar
  56. 56.
    Zhou, T., Tao, D., Wu, X.: Manifold elastic net: A unified framework for sparse dimension reduction. Data Min. Knowl. Discov. (2010) Google Scholar
  57. 57.
    Zhu, M., Martinez, A.M.: Subclass discriminant analysis. IEEE Trans. Pattern Anal. Mach. Intell. 28, 1274–1286 (2006) CrossRefGoogle Scholar
  58. 58.
    Zou, H., Hastie, T.: Regularization and variable selection via the Elastic Net. J. R. Stat. Soc. B 67, 301–320 (2005) MathSciNetMATHCrossRefGoogle Scholar
  59. 59.
    Zou, H., Hastie, T., Tibshirani, R.: Sparse principal component analysis. J. Comput. Graph. Stat. 15 (2004) Google Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Centre for Quantum Computation & Intelligence Systems, FEITUniversity of TechnologySydneyAustralia

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