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An Optimal Transformation for Discriminant and Principal Component Analysis
November 1988 (vol. 10 no. 6)
pp. 978-983

A general method is proposed to describe multivariate data sets using discriminant analysis and principal-component analysis. First, the problem of finding K discriminant vectors in an L-class data set is solved and compared to the solution proposed in the literature for two-class problems and the classical solution for L-class data sets. It is shown that the method proposed is better than the classical method for L classes and is a generalization of the optimal set of discriminant vectors proposed for two-class problems. Then the method is combined with a generalized principal-component analysis to permit the user to define the properties of each successive computed vector. All the methods were tested using measurements made on various kinds of flowers (IRIS data).

[1] H. Späth,Cluster Analysis Algorithms. New York: Wiley, 1980.
[2] J. A. Hartigan,Clustering Algorithms, J. Wiley: Ed., 1975.
[3] G. H. Ball and D. J. Hall, "A clustering technique for summarizing multivariate data,"Behavioral Sci., vol. 12, pp. 153-155, 1967.
[4] K. Fukunaga and W. L. G. Koontz, "Application of the Karhunen Loeve expansion to feature selection and ordering,"IEEE Trans. Comput., vol. C-19, no. 4, pp. 311-318, 1970.
[5] J. M. Romeder,Methodes et Programmes d'Analyse Discriminante. Paris: Dunod, 1973.
[6] C. R. Rao, "The use and interpretation of principal component analysis in applied research,"Sankhya Series A, vol. 26, pp. 329-357, 1964.
[7] T. Okada and S. Tomita, "An optimal orthonormal system for discriminant analysis,"Pattern Recognition, vol. 18, no. 2, pp. 139- 144, 1985.
[8] R. A. Fisher, "The use of multiple measurements in taxonomic problems,"Ann. Eugen., vol. 7, pp. 179-188, 1936.
[9] Y. T. Chien,Interactive Pattern Recognition. New York: Dekker, 1978.
[10] J. W. Sammon, "An optimal discriminant plane,"IEEE Trans. Comput., vol. C-19, pp. 826-829, 1970.
[11] D. H. Foley and J. W. Sammon, "An optimal set of discriminant vectors,"IEEE Trans. Comput., vol. C-24, pp. 281-289, 1975.
[12] J. Duchene, "A significant plane for two-class discrimination problems,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 557-559, 1986.
[13] T. W. Anderson and X. X. Bahadur, "Classification into two multivariate normal distributions with different covariance matrices,"Ann. Math. Stat., vol. 33, pp. 420-431, 1962.
[14] K. V. Mardia,Multivariate Analysis. London: Academic, 1979.
[15] G. B. Swas, A. K. Jain, and R. C. Dubes, "Evaluation of projection algorithms,"IEEE Trans. Pattern Anal. Machine Intell, vol. PAMI- 3, pp. 701-708, 1981.

Index Terms:
optimal transformation; principal component analysis; multivariate data sets; discriminant analysis; discriminant vectors; computerised pattern recognition; vectors
L. Duchene, S. Leclerq, "An Optimal Transformation for Discriminant and Principal Component Analysis," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 6, pp. 978-983, Nov. 1988, doi:10.1109/34.9121
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