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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
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)
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)
Aitken, C.G.G., Zadora, G., Lucy, D.: A two-level model for evidence evaluation. J. Forensic Sci. 52, 412–419 (2007)
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
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)
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)
Gao, Q.-X.: Is two-dimensional PCA equivalent to a special case of modular PCA? Pattern Recognit. Lett. 28(10), 1250–1251 (2007)
Gottumukkal, R., Asari, V.K.: An improved face recognition technique based on modular PCA approach. Pattern Recognit. Lett. 25(4), 429–436 (2004)
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)
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)
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)
Mardia, K.V., Kent, J.T., Bibby, J.M.: Multivariate Analysis. Academic Press, London (1979)
Martin, R.J.: A subclass of lattice processes applied to a problem in planar sampling. Biometrika 66(2), 209–217 (1979)
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)
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
Shen, L., Bai, L.: Mutualboost learning for selecting Gabor features for face recognition. Pattern Recognit. Lett. 27, 1758–1767 (2006)
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)
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)
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)
Ye, J.: Generalized low rank approximations of matrices. Mach. Learn. 61, 167–191 (2005)
Zhao, W., Chellappa, R., Phillips, J., Rosenfeld, A.: Face recognition: A literature survey. ACM Comput. Surv. 35, 399–458 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11222-008-9087-6