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Face Subspace Learning

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Handbook of Face Recognition

Abstract

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.

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References

  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)

    Article  Google Scholar 

  2. Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6), 1373–1396 (2003)

    Article  MATH  Google Scholar 

  3. Bian, W., Tao, D.: Harmonic mean for subspace selection. In: 19th International Conference on Pattern Recognition, pp. 1–4 (2008)

    Chapter  Google Scholar 

  4. Bian, W., Tao, D.: Manifold regularization for sir with rate root-n convergence (2010)

    Google Scholar 

  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. 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. 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. 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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  10. Decell, H., Mayekar, S.: Feature combinations and the divergence criterion. Comput. Math. Appl. 3(4), 71–76 (1977)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  13. Efron, B., Hastie, T., Johnstone, L., Tibshirani, R.: Least angle regression. Ann. Stat. 32, 407–499 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Fisher, R.A.: The use of multiple measurements in taxonomic problems. Ann. Eugen. 7, 179–188 (1936)

    Article  Google Scholar 

  15. Fukunaga, K.: Introduction to Statistical Pattern Recognition, 2nd edn. Academic Press, San Diego (1990)

    MATH  Google Scholar 

  16. Fukunaga, K., Mantock, J.: Nonparametric discriminant analysis. IEEE Trans. Pattern Anal. Mach. Intell. 5, 671–678 (1983)

    Article  MATH  Google Scholar 

  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. Hamsici, O.C., Martinez, A.M.: Bayes optimality in linear discriminant analysis. IEEE Trans. Pattern Anal. Mach. Intell. 30(4), 647–657 (2008)

    Article  Google Scholar 

  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. 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. He, X., Yan, S., Hu, Y., Niyogi, P.: Face recognition using Laplacianfaces. IEEE Trans. Pattern Anal. Mach. Intell. 27(3), 328–340 (2005)

    Article  Google Scholar 

  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. Jolliffe, I.: Principal Component Analysis, 2nd edn. Springer Series in Statistics, Springer, New York (2002)

    MATH  Google Scholar 

  24. Li, L.: Sparse sufficient dimension reduction. Biometrika 94(3), 603–613 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Li, S.Z.: Face recognition based on nearest linear combinations. In: CVPR, pp. 839–844 (1998)

    Google Scholar 

  26. Li, S.Z., Lu, J.: Face recognition using the nearest feature line method. IEEE Trans. Neural Netw. 10(2), 439–443 (1999)

    Article  Google Scholar 

  27. Li, Z., Lin, D., Tang, X.: Nonparametric discriminant analysis for face recognition. IEEE Trans. Pattern Anal. Mach. Intell. 31(4), 755–761 (2009)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  30. Lotlikar, R., Kothari, R.: Fractional-step dimensionality reduction. IEEE Trans. Pattern Anal. Mach. Intell. 22(6), 623–627 (2000)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    MATH  Google Scholar 

  34. Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)

    Article  Google Scholar 

  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. Schervish, M.: Linear discrimination for three known normal populations. J. Stat. Plan. Inference 10, 167–175 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  37. Shakhnarovich, G., Moghaddam, B.: Face recognition in subspaces. In: Handbook of Face Recognition, pp. 141–168 (2004)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  40. Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)

    Article  Google Scholar 

  41. Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc., Ser. B, Stat. Methodol. 58, 267–288 (1996)

    MathSciNet  MATH  Google Scholar 

  42. Tipping, M.E., Bishop, C.M.: Probabilistic principal component analysis. J. R. Stat. Soc., Ser. B, Stat. Methodol. 61(3), 611–622 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  43. Turk, M., Pentland, A.: Eigenfaces for recognition. J. Cogn. Neurosci. 3, 71–86 (1991)

    Article  Google Scholar 

  44. Wang, X., Tang, X.: A unified framework for subspace face recognition. IEEE Trans. Pattern Anal. Mach. Intell. 26, 1222–1228 (2004)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  46. Wang, X., Tang, X.: Random sampling for subspace face recognition. Int. J. Comput. Vis. 70, 91–104 (2006)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  49. Ye, J.: Least squares linear discriminant analysis. In: Proceedings of the 24th International Conference on Machine Learning, ICML ’07, pp. 1087–1093 (2007)

    Chapter  Google Scholar 

  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. Ye, J., Li, Q.: A two-stage linear discriminant analysis via qr-decomposition. IEEE Trans. Pattern Anal. Mach. Intell. 27(6), 929–941 (2005)

    Article  Google Scholar 

  52. Ye, J., Li, Q.: A two-stage linear discriminant analysis via qr-decomposition. IEEE Trans. Pattern Anal. Mach. Intell. 27, 929–941 (2005)

    Article  Google Scholar 

  53. Zhang, Z., Zha, H.: Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM J. Sci. Comput. 26, 313–338 (2005)

    Article  MathSciNet  Google Scholar 

  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. Zhang, T., Tao, D., Li, X., Yang, J.: Patch alignment for dimensionality reduction. IEEE Trans. Knowl. Data Eng. 21, 1299–1313 (2009)

    Article  Google Scholar 

  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. Zhu, M., Martinez, A.M.: Subclass discriminant analysis. IEEE Trans. Pattern Anal. Mach. Intell. 28, 1274–1286 (2006)

    Article  Google Scholar 

  58. Zou, H., Hastie, T.: Regularization and variable selection via the Elastic Net. J. R. Stat. Soc. B 67, 301–320 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  59. Zou, H., Hastie, T., Tibshirani, R.: Sparse principal component analysis. J. Comput. Graph. Stat. 15 (2004)

    Google Scholar 

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Acknowledgements

The authors thank Prof. Stan Z. Li for insightful discussions on nearest feature line.

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Authors and Affiliations

  1. Centre for Quantum Computation & Intelligence Systems, FEIT, University of Technology, Sydney, NSW, 2007, Australia

    Wei Bian & Dacheng Tao

Authors
  1. Wei Bian
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  2. Dacheng Tao
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Correspondence to Wei Bian .

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Editors and Affiliations

  1. Institute of Automation, Center Biometrics Research & Security, Chinese Academy of Science, Room 1227, Zhongguancun 95, Beijing Donglu, 100080, China, People's Republic

    Stan Z. Li

  2. Dept. Computer Science & Engineering, Michigan State University, East Lansing, 48824-1226, Michigan, USA

    Anil K. Jain

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Bian, W., Tao, D. (2011). Face Subspace Learning. In: Li, S., Jain, A. (eds) Handbook of Face Recognition. Springer, London. https://doi.org/10.1007/978-0-85729-932-1_3

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  • DOI: https://doi.org/10.1007/978-0-85729-932-1_3

  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-931-4

  • Online ISBN: 978-0-85729-932-1

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