Abstract
We construct a one-hidden-layer neural network capable of learning simultaneously several Bayesian discriminant functions and converting them to the corresponding Mahalanobis discriminant functions in the two-category, normal-distribution case. The Bayesian discriminant functions correspond to the respective situations on which the priors and means depend. The algorithm is characterized by the use of the inner potential of the output unit and additional several memory nodes. It is remarkably simpler when compared with our previous algorithm.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Funahashi, K.: Multilayer Neural Networks and Bayes Decision Theory. Neural Networks 11, 209–213 (1998)
Ito, Y., Srinivasan, C.: Multicategory Bayesian Decision Using a Three-layer Neural Network. In: Kaynak, O., Alpaydın, E., Oja, E., Xu, L. (eds.) ICANN 2003 and ICONIP 2003. LNCS, vol. 2714, pp. 253–261. Springer, Heidelberg (2003)
Ito, Y., Srinivasan, C.: Bayesian Decision Theory on Three-layer neural networks. Neurocomput. 63, 209–228 (2005)
Ito, Y., Srinivasan, C., Izumi, H.: Bayesian Learning of Neural Networks Adapted to Changes of Prior Probabilities. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds.) ICANN 2005. LNCS, vol. 3697, pp. 253–259. Springer, Heidelberg (2005)
Ito, Y., Srinivasan, C., Izumi, H.: Discriminant Analysis by a Neural Network with Mahalanobis Distance. In: Kollias, S.D., Stafylopatis, A., Duch, W., Oja, E. (eds.) ICANN 2006. LNCS, vol. 4132, pp. 350–360. Springer, Heidelberg (2006)
Ito, Y.: Simultaneous Approximations of Polynomials and Derivatives and Their Applications to Neural Networks. Neural Comput. 20, 2757–2791 (2008)
Ito, Y., Srinivasan, C., Izumi, H.: Learning of Bayesian Discriminant Functions by a Layered Neural Network. In: Ishikawa, M., Doya, K., Miyamoto, H., Yamakawa, T. (eds.) ICONIP 2007, Part I. LNCS, vol. 4984, pp. 238–247. Springer, Heidelberg (2008)
Ito, Y., Srinivasan, C., Izumi, H.: Multi-category Bayesian Decision by Neural Networks. In: Kůrková, V., Neruda, R., KoutnÃk, J. (eds.) ICANN 2008, Part I. LNCS, vol. 5163, pp. 21–30. Springer, Heidelberg (2008)
Ito, Y., Izumi, H., Srinivasan, C.: Learning of Mahalanobis Discriminant Functions by a Neural Network. In: Leung, C.S., Lee, M., Chan, J.H. (eds.) ICONIP 2009, Part I. LNCS, vol. 5863, pp. 417–424. Springer, Heidelberg (2009)
Ito, Y., Izumi, H., Srinivasan, C.: Simultaneous Learning of Several Bayesian and Mahalanobis Discriminant Functions by a Neural Network with Additional Nodes. Australian J. Intell. Inform. Process. Syst. 11, 1–7 (2010); Proceedings of ICONIP 2010
Ito, Y., Izumi, H., Srinivasan, C.: Learning of Mahalanobis Discriminant Functions by a Neural Network (submitted, preparation)
Richard, M.D., Lipmann, R.P.: Neural Network Classifiers Estimate Bayesian a Posteriori Probabilities. Neural Comput. 3, 461–483 (1991)
Ruck, M.D., Rogers, S., Kabrisky, M., Oxley, H., Sutter, B.: The Multilayer Perceptron as Approximator to a Bayes Optimal Discriminant Function. IEEE Trans. Neural Networks 1, 296–298 (1990)
White, H.: Learning in Artificial Neural Networks: A Statistical Perspective. Neural Comput. 1, 425–464 (1989)
Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. Joh Wiley & Sons, New York (1973)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ito, Y., Izumi, H., Srinivasan, C. (2012). Simultaneous Learning of Several Bayesian and Mahalanobis Discriminant Functions by a Neural Network with Memory Nodes. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds) Neural Information Processing. ICONIP 2012. Lecture Notes in Computer Science, vol 7667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34500-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-34500-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34499-2
Online ISBN: 978-3-642-34500-5
eBook Packages: Computer ScienceComputer Science (R0)