Abstract
LDA is popularly used in the pattern recognition field. Unfortunately LDA always confronts the small sample size problem (S3), which leads the within-class scatter matrix to be singular. In this case, PCA is always used for dimensional reduction to solve the problem in practice. This paper analyzes that when the small sample size problem happens, the PCA processing is not only to play the role of solving the S3 problem but also can be used to induce a fast calculation algorithm for solving the fisher criteria. This paper will show that calculating the eigenvectors of within-class scatter matrix after dimensional reduction can solve the optimal projection for fisher criteria.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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)
Jin, Z., Yang, J.Y., Tang, Z.M., Hu, Z.S.: A theorem on the uncorrelated optimal discriminant vectors. Pattern Recognition 34, 2041–2047 (2001)
Duchene, J., Leclercq, S.: An optimal transformation for discriminant and principal component analysis. IEEE Trans. Pattern Anal. Mach. Intell. 10(6), 978–983 (1988)
Martinez, A.M., Kak, A.C.: PCA Versus LDA. IEEE Trans. Pattern Anal. Mach. Intell. 23(2), 228–233 (2001)
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(10), 1090–1103 (2000)
Fisher, R.A.: The Use of Multiple Measures in Taxonomic Problems. Ann. Eugenics 7, 179–188 (1936)
Ye, J.P., Janardan, R., Park, C.H., Park, H.: An Optimization Criterion for Generalized Discriminant Analysis on Undersampled Problems. IEEE Trans. Pattern Anal. Mach. Intell. 26(8), 982–994 (2004)
Zhao, W., Chellappa, R., Phillips, J., Rosenfeld, A.: Face Recognition: A Literature Survey. ACM Computing Surveys 35(4), 399–458 (2003)
Ye, J.P., Li, Q.: LDA/QR: an efficient and effective dimension reduction algorithm and its theoretical foundation. Pattern Recognition 37(4), 851–854 (2004)
Zhao, W., Chellappa, R., Phillips, P.J.: Subspace linear discriminant analysis for face recognition. Technical Report CAR-TR-914, CS-TR-4009, University of Maryland at College Park, USA
Phillips, P.J., Grother, P., Micheals, R., Blackburn, D.M., Tabassi, E., Bone, J.M.: Face Recognition Vendor Test 2002: Evaluation Results. Available at, http://www.frvt.org/DLs/FRVT_2002_Evaluation_Report.pdf
Wang, X.G., Tang, X.O.: A Unified Framework for Subspace Face Recognition. IEEE Trans. PAMI 26(9), 1222–1228 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zheng, W., Lai, J., Yuen, P.C. (2004). Fast Calculation for Fisher Criteria in Small Sample Size Problem. In: Li, S.Z., Lai, J., Tan, T., Feng, G., Wang, Y. (eds) Advances in Biometric Person Authentication. SINOBIOMETRICS 2004. Lecture Notes in Computer Science, vol 3338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30548-4_38
Download citation
DOI: https://doi.org/10.1007/978-3-540-30548-4_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24029-7
Online ISBN: 978-3-540-30548-4
eBook Packages: Computer ScienceComputer Science (R0)