×

Application of constrained generalized inverse to pattern classification. (English) Zbl 0356.62051

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Al-Alaoui, M. A., Some Applications of Generalized Inverse to Pattern Recognition, (Ph.D. Thesis (December 1974), Electrical Engineering Department, Georgia Institute of Technology)
[2] Albert, A., Regression and the Moore-Penrose Pseudo-Inverse (1972), Academic Press: Academic Press NY
[3] Anderson, T. W., An Introduction to Multivariate Statistical Analysis (1957), Wiley: Wiley NY
[4] Andrews, H. C., Introduction to Mathematical Techniques in Pattern Recognition (1972), Wiley: Wiley NY · Zbl 0258.68053
[5] Ben-Israel, A.; Greville, T. N.E., Generalized Inverses: Theory and Applications (1974), Wiley: Wiley NY · Zbl 0305.15001
[6] Bjerhammer, A., Theory of Errors and Generalized Matrix Inverses (1973), Elsevier: Elsevier NY
[7] Boullion, T. L.; Odell, P. L., Generalized Inverse Matrices (1971), Wiley: Wiley NY · Zbl 0223.15002
[8] Duda, R. O.; Hart, P. E., Pattern Classification and Scene Analysis (1973), Wiley: Wiley NY · Zbl 0277.68056
[9] Fisher, R. A., Contributions to Mathematical Statistics (1950), Wiley: Wiley NY · Zbl 0040.36201
[10] Fu, K. S., Sequential Methods in Pattern Recognition and Machine Learning (1968), Academic Press: Academic Press NY · Zbl 0188.52303
[11] Ho, Y. C.; Kashyap, R. L., An algorithm for linear inequalities and its applications, IEEE Trans. Elec. Comp., 14, 683-688 (1965) · Zbl 0173.17902
[12] Koford, J. S.; Groner, G. F., The use of an adaptive threshold element to design a linear optimal pattern classifier, IEEE Trans. Info. Theory, 12, 42-50 (January 1966)
[13] Luenberger, D. G., Optimization by Vector Space Methods (1969), Wiley: Wiley NY · Zbl 0176.12701
[14] Minamide, N.; Nakamura, K., A restricted pseudo inverse and its application to constrained minima, SIAM Journal on Applied Mathematics, 19, 1 (July 1970)
[15] Nashed, M. Z., Generalized inverses, normal solvability, and iteration for singular operator equations, (Rall, L. B., Nonlinear Functional Analysis and Applications (1971), Academic Press: Academic Press NY), 311-359 · Zbl 0236.41015
[16] Nilsson, N. J., Learning Machines (1965), McGraw-Hill: McGraw-Hill NY · Zbl 0152.35705
[17] Noble, B., Computational methods for generalized inverses of matrices and related results, (Nashed, M. Z., Generalized Inverses, Theory and Applications (1976), Academic Press: Academic Press NY)
[18] Patterson, J. D.; Womack, B. F., An adaptive pattern classification system, IEEE Trans. Sys. Sci. Cyb., 2, 62-67 (August 1966)
[19] Penrose, R., A generalized inverse for matrices, (Proc. Cambridge Philos. Soc., 51 (1955)), 406-413 · Zbl 0065.24603
[20] Penrose, R., On best approximate solution of linear matrix equations, (Proc. Cambridge Philos. Soc., 52 (1956)), 17-19 · Zbl 0070.12501
[21] Peterson, D. W.; Mattson, R. L., A method of finding linear discriminant functions for a class of performance criteria, IEEE Trans. Info. Theory, 12, 380-387 (1966) · Zbl 0151.22904
[22] Pringle, R. M.; Rayner, A. A., Generalized Inverse Matrices with Applications to Statistics (1971), Griffin: Griffin London · Zbl 0231.15008
[23] Rao, C. R.; Mitra, S. K., Generalized Inverse of Matrices and Its Applications (1971), Wiley: Wiley NY
[24] Sebestyen, G. D.; Edie, J., An algorithm for nonparametric pattern recognition, IEEE Trans. Electronic Computers, 15, 908-915 (1966)
[25] Shinozaki, N., Numerical algorithms for the Moore-Penrose inverse of a matrix: Direct methods, Ann. Inst. Stat. Math., 24, 1, 193-203 (1972)
[26] Shinozaki, N., Numerical algorithms for the Moore-Penrose inverse of a matrix: Iterative methods, Ann. Inst. Stat. Math., 24, 3 (1972)
[27] Smith, F. W., Design of minimum-error optimal classifiers for patterns from distributions with Gaussian tails, IEEE Trans. Info. Theory, 17, 6, 701-707 (November 1971)
[28] Smith, F. W., Small-sample optimality of design techniques for linear classifiers of Gaussian patterns, IEEE Trans. Info. Theory, 18, 1, 118-126 (January 1972)
[29] Stewart, G. W., Introduction to Matrix Computations (1973), Academic Press: Academic Press NY · Zbl 0302.65021
[30] Theil, H., Principles of Econometrices (1971), Wiley: Wiley NY
[31] Wee, W. G., Generalized inverse approach to adaptive multiclass patterns classification, IEEE Trans. Comput., 17, 1157-1164 (1968) · Zbl 0181.22504
[32] Wee, W. G., Generalized inverse approach to clustering, feature selection, and classification, IEEE Trans. Info. Theory, 17, 3, 262-269 (May 1971)
[33] Wee, W. G., On feature selection in a class of distribution-free pattern classifiers, IEEE Trans. on Info. Theory, 16, 1, 47-55 (January 1970)
[34] Wee, W. G.; Fu, K. S., An extension of the generalized inverse algorithm to multiclass pattern classification, (IEEE Trans. on Systems Science and Cybernetics (July 1968)), 192-194
[35] Wilkinson, J. H.; Reinsch, C., (Handbook for Automatic Computation, Vol. II, Linear Algebra (1971), Springer: Springer NY)
[36] Yau, S. S.; Garnett, J. M., Least-mean-square approach to pattern classification, (Watanabe, M. S., Frontiers of Pattern Recognition (1972), Academic Press: Academic Press NY), 575-587 · Zbl 0257.68105
[37] Young, T. Y.; Calvert, T. W., Classification, Estimation and Pattern Recognition (1974), American Elsevier: American Elsevier NY · Zbl 0277.68055
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.