# On the Capability of Neural Networks to Approximate the Neyman-Pearson Detector - A Theoretical Study

### P. Jarabo-Amores, R. Gil-Pita, M. Rosa-Zurera, F. López-Ferreras

#### Abstract

In this paper, the application of neural networks for approximating the Neyman-Pearson detector is considered. We propose a strategy to identify the training parameters that can be controlled for reducing the effect of approximation errors over the performance of the neural network based detector. The function approximated by a neural network trained using the mean squared-error criterion is deduced, without imposing any restriction on the prior probabilities of the clases and on the desired outputs selected for training, proving that these parameters play an important role in controlling the sensibility of the neural network detector performance to approximation errors. Another important parameter is the signal-to-noise ratio selected for training. The proposed strategy allows to determine its best value, when the statistical properties of the feature vectors are known. As an example, the detection of gaussian signals in gaussian interference is considered.

#### References

- Van Trees, H.L.: Detection, estimation, and modulation theory, Vol. 1. Wiley, (1968)
- Ruck, D.W., Rogers, S.K., Kabrisky, M., Oxley, M.E., Suter, B.W.: The multilayer perceptron as an aproximation to a Bayes optimal discriminant function. IEEE Transactions on Neural Networks, vol. 1, no. 4, 296-298, December 1990.
- Wan, E.A.: Neural Network Classi cation: A Bayesian Interpretation. IEEE Transactions on Neural Networks, vol.1, no. 4, pp. 303-305, December 1990.
- Gandhi, P.P., Ramamurti, V.: Neural networks for signal detection in non-gaussian noise. IEEE Transactions on signal processing, vol. 45, no. 11, pp. 2846-2851, November 1997.
- Andina, D., Sanz-Gonz=E1lez, J.L.: Comparison of a neural network detector vs. NeymanPearson optimal detector. Proceedings of the 1996 IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 6, pp. 3573-3576, 1995.
- Jarabo-Amores, P., Rosa-Zurera, M., López Ferreras, F.: Design of a Pre-processing Stage for Avoiding the Dependence on TSNR of a Neural Radar Detector. Lecture Notes in Computer Sciences, Vol. 2085. Springer-Verlag, Berlin Heidelberg New York (2001) 652-659,

#### Paper Citation

#### in Harvard Style

Jarabo-Amores P., Gil-Pita R., Rosa-Zurera M. and López-Ferreras F. (2004). **On the Capability of Neural Networks to Approximate the Neyman-Pearson Detector - A Theoretical Study** . In *Proceedings of the First International Workshop on Artificial Neural Networks: Data Preparation Techniques and Application Development - Volume 1: ANNs, (ICINCO 2004)* ISBN 972-8865-14-7, pages 67-74. DOI: 10.5220/0001150100670074

#### in Bibtex Style

@conference{anns04,

author={P. Jarabo-Amores and R. Gil-Pita and M. Rosa-Zurera and F. López-Ferreras},

title={On the Capability of Neural Networks to Approximate the Neyman-Pearson Detector - A Theoretical Study},

booktitle={Proceedings of the First International Workshop on Artificial Neural Networks: Data Preparation Techniques and Application Development - Volume 1: ANNs, (ICINCO 2004)},

year={2004},

pages={67-74},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001150100670074},

isbn={972-8865-14-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the First International Workshop on Artificial Neural Networks: Data Preparation Techniques and Application Development - Volume 1: ANNs, (ICINCO 2004)

TI - On the Capability of Neural Networks to Approximate the Neyman-Pearson Detector - A Theoretical Study

SN - 972-8865-14-7

AU - Jarabo-Amores P.

AU - Gil-Pita R.

AU - Rosa-Zurera M.

AU - López-Ferreras F.

PY - 2004

SP - 67

EP - 74

DO - 10.5220/0001150100670074