Abstract
We propose a neural network which can approximate Mahalanobis discriminant functions after being trained. It can be realized if a Bayesian neural network is equipped with two additional subnetworks. The training is performed sequentially and, hence, the past teacher signals need not be memorized. In this paper, we treat the two-category normal-distribution case. The results of simple simulations are included.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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
Duda, R.O., Hart, P.E.: Pattern classification and scene analysis. Joh Wiley & Sons, New York (1973)
Funahashi, K.: Multilayer neural networks and Bayes decision theory. Neural Networks 11, 209–213 (1998)
Ito, Y.: Simultaneous L p -approximations of polynomials and derivatives on Rd and their applications to neural networks (in preparation)
Ito, Y., Srinivasan, C.: Multicategory Bayesian decision using a three-layer neural network. In: Proceedings of ICANN/ICONIP 2003, pp. 253–261 (2003)
Ito, Y., Srinivasan, C.: Bayesian decision theory on three-layer neural networks. Neurocomputing 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)
Richard, M.D., Lipmann, R.P.: Neural network classifiers estimate Bayesian a posteriori probabilities. Neural Computation 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 Transactions on Neural Networks 1, 296–298 (1990)
White, H.: Learning in artificial neural networks: A statistical perseptive. Neural Computation 1, 425–464 (1989)
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
Ito, Y., Srinivasan, C., Izumi, H. (2006). Discriminant Analysis by a Neural Network with Mahalanobis Distance. In: Kollias, S., Stafylopatis, A., Duch, W., Oja, E. (eds) Artificial Neural Networks – ICANN 2006. ICANN 2006. Lecture Notes in Computer Science, vol 4132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11840930_36
Download citation
DOI: https://doi.org/10.1007/11840930_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38871-5
Online ISBN: 978-3-540-38873-9
eBook Packages: Computer ScienceComputer Science (R0)