A theorem on the uncorrelated optimal discriminant vectors. (English) Zbl 0999.68189

Summary: This paper proposes a theorem on the Uncorrelated Optimal Discriminant Vectors (UODVs). It is proved that the classical optimal discriminant vectors are equivalent to UODV, which can be used to extract \((L-1)\) uncorrelated discriminant features for \(L\)-class problems without losing any discriminant information in the meaning of Fisher discriminant criterion function. Experiments on Concordia University CENPARMI handwritten numeral database indicate that UODVs are much more powerful than the Foley-Sammon optimal discriminant vectors. It is believed that when the number of training samples is large, the conjugate orthogonal set of discriminant vectors can be much more powerful than the orthogonal set of discriminant vectors.


68T10 Pattern recognition, speech recognition


Full Text: DOI


[1] Fisher, R.A., The use of multiple measurements in taxonomic problems, Ann. eugenics, 7, 178-188, (1936)
[2] S.S. Wilks, Mathematical Statistics, Wiley, New York, 1962, pp. 577-578. · Zbl 0173.45805
[3] Duda, R.O.; Hart, P.E., Pattern classification and scene analysis, (1973), Wiley New York · Zbl 0277.68056
[4] Sammon, J.W., An optimal transformation plane, IEEE trans. comput., 19, 9, 826-829, (1970) · Zbl 0205.17906
[5] Foley, D.H.; Sammon, J.W., An optimal set of discriminant vectors, IEEE trans. comput., 24, 3, 281-289, (1975) · Zbl 0296.68106
[6] Kittler, J.; Young, P.C., A new approach to feature selection based on the Karhunen-loeve expansion, Pattern recognition, 5, 335-352, (1973)
[7] Kittler, J., On the discriminant vector method of feature selection, IEEE trans. comput., 26, 6, 604-606, (1977)
[8] Okada, T.; Tomita, S., An optimal orthonormal system for discriminant analysis, Pattern recognition, 18, 2, 139-144, (1985)
[9] Duchene, J.; Leclercq, S., An optimal transformation for discriminant and principal component analysis, IEEE trans. pattern anal. Mach. intell., 10, 6, 978-983, (1988) · Zbl 0655.62064
[10] Y. Hamamoto, T. Kanaoka, S. Tomita, Orthogonal discriminant analysis for interactive pattern analysis, Proceedings Tenth International Conference on Pattern Recognition, 1990, pp. 424-427.
[11] Hamamoto, Y.; Matsuura, Y.; Kanaoka, T.; Tomita, S., A note on the orthonormal discriminant vector method for feature extraction, Pattern recognition, 24, 7, 681-684, (1991)
[12] Longstaff, I.D., On extensions to Fisher’s linear discriminant function, IEEE trans. pattern anal. Mach. intell., 9, 2, 321-324, (1987)
[13] Liu, K.; Cheng, Y.Q.; Yang, J.Y., A generalized optimal set of discriminant vectors, Pattern recognition, 25, 7, 731-739, (1992)
[14] Jin, Z.; Lou, Z.; Yang, J.Y., An optimal discriminant plane with uncorrelated features, Pattern recognition artifi. intell., 12, 3, 334-339, (1999), (in Chinese)
[15] Jin, Z.; Yang, J.Y.; Lu, J.F., An optimal set of uncorrelated discriminant features, Chinese J. comput., 22, 10, 1105-1108, (1999), (in Chinese)
[16] Z. Jin, J.Y. Yang, Z.S. Hu, Z. Lou, Face recognition based on the uncorrelated discriminant transformation, Pattern Recognition, to appear. · Zbl 0978.68118
[17] Hughes, G.F., On the Mean accuracy of statistical pattern recognizers, IEEE trans. inform. theory, 14, 1, 55-63, (1968)
[18] Fukunaga, K., Introduction to statistical pattern recognition, (1990), Academic Press New York · Zbl 0711.62052
[19] Hu, Z.S.; Lou, Z.; Yang, J.Y.; Liu, K.; Suen, C.Y., Handwritten digit recognition based on multi-classifier combination, Chinese J. comput., 22, 4, 369-374, (1999), (in Chinese)
[20] H. Yoshihiko et al. Recognition of handwritten numerals using Gabor features, Proceedings of the Thirteenth ICPR, pp. 250-253.
[21] Liao, S.X.; Pawlak, M., On image analysis by moments, IEEE trans. pattern anal. machine intell., 18, 3, 254-266, (1996)
[22] Bailey, R.R.; Mandyam, S., Orthogonal moment feature for use with parametric and non-parametric classifiers, IEEE trans. pattern anal. Mach. intell., 18, 4, 389-398, (1996)
[23] Alireza, K.; Yawhua, H., Invariant image recognition by Zernike moments, IEEE trans. pattern anal. Mach. intell., 12, 489-497, (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.