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Factored principal components analysis, with applications to face recognition

Abstract

A dimension reduction technique is proposed for matrix data, with applications to face recognition from images. In particular, we propose a factored covariance model for the data under study, estimate the parameters using maximum likelihood, and then carry out eigendecompositions of the estimated covariance matrix. We call the resulting method factored principal components analysis. We also develop a method for classification using a likelihood ratio criterion, which has previously been used for evaluating the strength of forensic evidence. The methodology is illustrated with applications in face recognition.

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References

  • Aitken, C.G.G., Lucy, D.: Evaluation of trace evidence in the form of multivariate data. J. R. Stat. Soc. Ser. C 53(1), 109–122 (2004)

    MATH  Article  MathSciNet  Google Scholar 

  • Aitken, C.G.G., Lucy, D., Zadora, G., Curran, J.M.: Evaluation of transfer evidence for three-level multivariate data with the use of graphical models. Comput. Stat. Data Anal. 50(10), 2571–2588 (2006)

    MATH  Article  MathSciNet  Google Scholar 

  • Aitken, C.G.G., Zadora, G., Lucy, D.: A two-level model for evidence evaluation. J. Forensic Sci. 52, 412–419 (2007)

    Article  Google Scholar 

  • Bai, L., Shen, L., Wang, Y.: A novel eye location algorithm based on radial symmetry transform. In: 18th International Conference on Pattern Recognition (ICPR 2006), 20–24 August 2006, Hong Kong, China, vol. 3, pp. 511–514. IEEE Computer Society (2006). ISBN 0-7695-2521-0

  • Bailly-Bailliére, E., Bengio, S., Bimbot, F., Hamouz, M., Kittler, J., Mariéthoz, J., Matas, J., Messer, K., Popovici, V., Porée, F., Ruíz, B., Thiran, J.-P.: The Banca database and evaluation protocol. In: Kittler, J., Nixon, M.S. (eds.) Audio- and Video-Based Biometric Person Authentication, 4th International Conference (AVBPA 2003) Proceedings, Guildford, UK, 9–11 June 2003. Lecture Notes in Computer Science, vol. 2688, pp. 625–638. Springer, Berlin (2003). ISBN 3-540-40302-7

    Chapter  Google Scholar 

  • Brignell, C.J.: Shape analysis and statistical modelling in brain imaging. Ph.D. thesis, University of Nottingham (2007)

  • Bruce, V., Young, A.: Understanding face recognition. Br. J. Psychol. 77, 305–327 (1986)

    Google Scholar 

  • Chang, C.-C., Lin, C.-J.: LIBSVM: a library for support vector machines, Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm (2001)

  • Dutilleul, P.: The MLE algorithm for the matrix normal distribution, J. Stat. Comput. Simul., 105–123 (1999)

  • Galecki, A.: General class of covariance structures for two or more repeated factors in longitudinal data analysis. Commun. Stat. Theory Methods 23, 3105–3119 (1994)

    MATH  Article  Google Scholar 

  • Gao, Q.-X.: Is two-dimensional PCA equivalent to a special case of modular PCA? Pattern Recognit. Lett. 28(10), 1250–1251 (2007)

    Article  Google Scholar 

  • Gottumukkal, R., Asari, V.K.: An improved face recognition technique based on modular PCA approach. Pattern Recognit. Lett. 25(4), 429–436 (2004)

    Article  Google Scholar 

  • Kong, H., Wang, L., Teoh, E.K., Li, X., Wang, J.-G., Venkateswarlu, R.: Generalized 2D principal component analysis for face image representation and recognition. Neural Netw. 18(56), 585–594 (2005)

    Article  Google Scholar 

  • Lanitis, A., Taylor, C.J., Cootes, T.F.: Automatic interpretation and coding of face images using flexible models. IEEE Trans. Pattern Anal. Mach. Intell. 19(7), 743–756 (1997)

    Article  Google Scholar 

  • Mardia, K.V., Goodall, C.R.: Spatial-temporal analysis of multivariate environmental monitoring data. In: Patil, G.P., Rao, C.R. (eds.) Multivariate Environmental Statistics. North-Holland, Amsterdam (1993)

    Google Scholar 

  • Mardia, K.V., Kent, J.T., Bibby, J.M.: Multivariate Analysis. Academic Press, London (1979)

    MATH  Google Scholar 

  • Martin, R.J.: A subclass of lattice processes applied to a problem in planar sampling. Biometrika 66(2), 209–217 (1979)

    MATH  Article  MathSciNet  Google Scholar 

  • Phillips, P.J., Moon, H., Rauss, P.J., Rizvi, S.: The FERET evaluation methodology for face recognition algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 22, 1090–1104 (2000)

    Article  Google Scholar 

  • Rangarajan, A.: Learning matrix space image representations. In: Figueiredo, M.A.T., Zerubia, J., Jain, A.K. (eds.) Energy Minimization Methods in Computer Vision and Pattern Recognition, Third International Workshop (EMMCVPR 2001) Proccedings, Sophia Antipolis, France, 3–5 September 2001. Lecture Notes in Computer Science, vol. 2134, pp. 153–168. Springer, Berlin (2001). ISBN 3-540-42523-3

    Chapter  Google Scholar 

  • Shen, L., Bai, L.: Mutualboost learning for selecting Gabor features for face recognition. Pattern Recognit. Lett. 27, 1758–1767 (2006)

    Article  Google Scholar 

  • Sinha, P., Balas, B.J., Ostrovsky, Y., Russel, R.: Face recognition by humans. In: Zhao, W., Chellappa, R. (eds.) Face Processing: Advanced Modeling and Methods. Academic Press, San Diego (2006)

    Google Scholar 

  • Vasilescu, M.A.O., Terzopoulos, D.: Multilinear subspace analysis of image ensembles. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2003), Madison, WI, USA, 16–22 June 2003, vol. 2, pp. 93–99. IEEE Computer Society (2003). ISBN 0-7695-1900-8

  • Wiskott, L., Fellous, J.-M., Kruger, N., von der Malsburg, C.: Face recognition by elastic bunch graph matching. IEEE Trans. Pattern Anal. Mach. Intell. 19(7), 775–779 (1997)

    Article  Google Scholar 

  • Yang, J., Zhang, D., Frangi, A.F., Yang, J.-Y.: Two-dimensional PCA: A new approach to appearance-based face representation and recognition. IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 131–137 (2004)

    Article  Google Scholar 

  • Ye, J.: Generalized low rank approximations of matrices. Mach. Learn. 61, 167–191 (2005)

    MATH  Article  Google Scholar 

  • Zhao, W., Chellappa, R., Phillips, J., Rosenfeld, A.: Face recognition: A literature survey. ACM Comput. Surv. 35, 399–458 (2003)

    Article  Google Scholar 

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Correspondence to Ian L. Dryden.

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Dryden, I.L., Bai, L., Brignell, C.J. et al. Factored principal components analysis, with applications to face recognition. Stat Comput 19, 229–238 (2009). https://doi.org/10.1007/s11222-008-9087-6

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  • DOI: https://doi.org/10.1007/s11222-008-9087-6

Keywords

  • Face recognition
  • Forensic identification
  • Gabor wavelets
  • Kernel density estimator
  • Likelihood ratio
  • Multivariate normal
  • Principal components analysis