Abstract
Equation for generalization error of Multinomial classifier is derived and tested. Particular attention is paid to imbalanced training sets. It is shown that artificial growth of training vectors of less probable class could be harmful. Use of predictive Bayes approach to estimate cell probabilities of the classifier reduces both the generalization error and effect of unequal training sample sizes.
Chapter PDF
Similar content being viewed by others
Keywords
References
Lachenbruch, P.A., Goldstein, M.: Discriminant analysis. Biometrics 5(3), 9–85 (1979)
Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. Wiley, New York (2000)
Hughes, G.F.: On the mean accuracy of statistical pattern recognizers. IEEE Trans. on Information Theory IT-14, 55–63 (1965)
Chandrasekaran, B., Jain, A.K.: Quantization complexity and independent measurements. IEEE Trans. Computers 23, 102–106 (1974)
Duin, R.P.W.: On the Accuracy of Satistical Pattern Recognizers. Ph.D. dissertation. Delft University of Technology, Delft (1978)
Griskevicius, D., Raudys, S.: On the expected probability of the classification error of the classifier for discrete variables. In: Raudys, S. (ed.) Statistical Problems of Control. Institute of Mathematics and Informatics, Vilnius, vol. 38, pp. 95–112 (1979) (in Russian)
Serych, A.P.: On use of nonparametric density estimates in pattern recognition. In: Proc. of Siberian Physic technical V.D. Kuznetsov Institute, vol. 63, pp. 13–41 (1973) (in Russian)
Raudys, S.: Statistical and Neural Classifiers: An integrated approach to design, p. 312. Springer, New York (2000)
Amari, S.: A universal theorem on learning curves. Neural Networks 6, 161–166 (1993)
Vidyasagar, M.: A Theory of Learning and Generalization. Springer, London (1997)
Vapnik, V.: Statistical Learning Theory. John Wiley and Sons, New York (1998)
Skurichina, M., Raudys, S., Duin, R.P.W.: K-NN directed noise injection in multilayer perceptron training. IEEE Trans. on Neural Networks 11(2), 504–511 (2000)
Raudys, S.: Experts’ boasting in trainable fusion rule. IEEE Trans. on Pattern Analysis and Machine Intelligence, PAMI 25(9), 1178–1182 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Raudys, S. (2006). Generalization Error of Multinomial Classifier. In: Yeung, DY., Kwok, J.T., Fred, A., Roli, F., de Ridder, D. (eds) Structural, Syntactic, and Statistical Pattern Recognition. SSPR /SPR 2006. Lecture Notes in Computer Science, vol 4109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11815921_55
Download citation
DOI: https://doi.org/10.1007/11815921_55
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37236-3
Online ISBN: 978-3-540-37241-7
eBook Packages: Computer ScienceComputer Science (R0)