Synonym
Definition
Linear dimension reduction technique reduces the dimension of biometric data using a linear transform. The linear transform is always learned by optimization of a criterion. Biometric data are then projected on to the range space of this transform. Subsequent processing is then performed in that lower-dimensional space.
Introduction
In biometrics, data are invariably represented in vectors and the dimensionality is consistently very high. It would be computationally expensive to process them directly by using many algorithms. Moreover, it is sometimes desirable to exact robust, informative or discriminative facts contained in the data. For these reasons, a lower dimensional subspace is found such that the most important part of the data is retained for linear representation. Among the techniques for learning such subspace, linear dimension reduction methods are popular.
Given a set of N data samples {x 1, … , x N }, where x i  ∈ \(\Re\)...
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References
Turk, M., Pentland, A.: Eigenfaces for recognition. J. Cogn. Neurosci. 3(1), 71–86 (1991)
Hyvärinen, A., Oja, E.: Independent component analysis: algorithms and applications. Neural Networks 13, 411–430 (2000)
Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401, 788–791 (1999)
Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. In: Advances in Neural Information Processing Systems, Denver, Colorado pp. 556–562 (2000)
He, X., Niyogi, P.: Locality preserving projections. In: Advances in Neural Information Processing Systems, Vancauver, Canada pp. 153–160 (2003)
A., F.R.: The Use of Multiple Measures in Taxonomic Problems. Ann. Fisher, RA Eugenics 7, 179–188 (1936)
Belhumeour, P.N., Hespanha, J.P., Kriegman, D.J.: Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans. Pattern Analy. Mach. Intell. 19(7), 711–720 (1997)
Chen, L.F., Liao, H.Y.M., Ko, M.T., Lin, J.C., Yu, G.J.: A new LDA-based face recognition system which can solve the small sample size problem. Pattern Recogn. 33, 1713–1726 (2000)
Webb, A.R. (ed.): Statistical Pattern Recognition, 2nd ed. 2002. Wiley, England (2002)
Li, H., Jiang, T., Zhang, K. Efficient and robust feature extraction by maximum margin criterion. IEEE Trans. Neural Networks 17(1), 157–165 (2006)
MartÃnez, A.M., Kak, A.C.: PCA versus LDA. IEEE Trans. Pattern Analy. Mach. Intell. 23(2), 228–233 (2001)
Cai, D., He, X., Han, J.: Semi-supervised Discriminant Analysis. In: IEEE Int. Conf. Comput. Vis. Rio de Janeiro, Brazil (2007)
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 Analy. Mach. Intell. 26(1), 131–137 (2004)
Xiong, H., Swamy, M.N.S., Ahmad, M.O.: Two-dimensional FLD for face recognition. Pattern Recogn. 38, 1121–1124 (2005)
Kong, H., Li, X., Wang, L., Teoh, E.K., J.-G., W., Venkateswarlu, R.: Generalized 2D principal component analysis. In: IEEE International Joint Conference on Neural Networks, vol. 1, pp. 108–113. Oxford, UK (2005)
Ye, J.P., Janardan, R., Li, Q.: Two-dimensional linear discriminant analysis. In: Advances in Neural Information Processing Systems, pp. 1569–1576 (2004)
Zheng, W.S., Lai, J.H., Li, S.Z.: 1D-LDA versus 2D-LDA: when is vector-based linear discriminant analysis better than matrix-based? Pattern Recogn. 41(7), 2156–2172 (2008)
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Zheng, WS., Lai, J.H., Yuen, P.C. (2009). Linear Dimension Reduction. In: Li, S.Z., Jain, A. (eds) Encyclopedia of Biometrics. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-73003-5_296
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DOI: https://doi.org/10.1007/978-0-387-73003-5_296
Publisher Name: Springer, Boston, MA
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