Neural networks suitable for law discovery tasks

• Autorzy: Majewski J. , Wojtyna R.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we discuss a possibility of using special-type neural networks to extract laws governing a given set of empirical numerical data. Our considerations are an expansion of the idea proposed in [2] and extended in [3, 4]. We propose several neural networks modeling various relations between these data. One group create networks modeling relations of a polynomial type, another networks dealing with reciprocal descriptions and yet another with fractional rational relationships. The latter case means relations described by a ratio of two polynomials. In the network connected with polynomial relations, ln(.) and exp(.) functions are used as the network activation functions, like in [3]. The difference between the proposed network and the one presented in [3] is that in our network the ln(.) function operates in a hidden layer, while in [3] it operates directly on input variables. The second proposed network, being an entirely new solution, concerns reciprocal descriptions and utilizes functions of a 1/(.) type to realize the activation tasks. Apart from the above mentioned networks, also some novel neural networks, suitable for problems described by ratio of two polynomials, are proposed. This extends the range of issues treated by our networks considerably because a lot of problems can be described in such a way. The achieved law extraction ability of all networks presented in this paper results from choosing proper network topologies and applying proper activation functions in proper places. The law discovery is carried out by learning the network and means obtaining information about parameters of the functions used to describe relations between the given numerical data. Theoretical descriptions as well as simulation results have been presented.

Słowa kluczowe

EN

law discovery; symbolic function extraction; neural networks

• Wydawca: Instytut Telekomunikacji i Informatyki Uniwersytetu Technologiczno-Przyrodniczego w Bydgoszczy
• Czasopismo: Image Processing & Communications
• Rocznik: 2010
• Tom: Vol. 15, no 2
• Strony: 17--25
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Majewski J.

autor

Wojtyna R.

• Institute of Telecommunication, UTP Bydgoszcz, Poland Kaliskiego 7, 85-796 Bydgoszcz,

Bibliografia

• [1] L. M. Fu. Knowledge Discovery by Inductive Neural Networks, IEEE Trans. On Knowledge and Data Engineering, Vol. 11, No. 6, November/December 1999.
• [2] R. Durbin, D. Rumelhart. Product Units: A Computationally Powerful and Biologically Plausible Extension to Backpropagation Networks, Neural Computation, Vol. 1, pp. 133-142, 1989.
• [3] K. Saito, R. Nakano. Law Discovery using neural networks, Proc. of the 15th International Joint Conference on Artificial Intelligence (IJCAI97), pp. 1078-1083, 1997.
• [4] A. Ismail, A. P. Engelbrecht. Paining Product Units in Feedforward Neural Networks using Particle Swarm Optimization, In: Development and Practice of Artificial Intelligence Techniques, V.B. Bajic, D. Sha (eds), Proceedings of the International Conference on Artificial Intelligence, Durban, South Africa, pp. 36-40, 1999.
• [5] A. B. Tickle, R. Andrews, M. Golea, J. Diederich. The Truth Will Come to Light: Directions and Challenges in Extracting the Knowledge Embedded Within Trained Artificial Neural Networks, IEEE Trans, on Neural Networks, Vol. 9, No. 6, November 1998.
• [6] L. M. Fu. Learning in Certainty-Factor-Based Multilayer Neural Networks for Classification, IEEE Trans, on Neural Networks, Vol. 9, No. 1, January 1998.
• [7] T. Washio, H. Motoda, Y. Niwa. Enhancing the Plausibility of Law Equation Discovery, Proc. ICML2000, pp. 1127-1134, 2000.
• [8] T. Washio, H. Motoda, Y. Niwa. Discovering Admissible Simultaneous Equation Models from Observed Data, LNCS 2167, Springer-Verlag, Berlin Heidelberg, pp. 539-551, 2001.
• [9] J. Majewski, R. Wojtyna. Extracting symbolic function expressions by means of neural networks, In: R. S. Choras (Ed.): Image Processing and Communication Challenges 2, Advances in Soft Computing, 323-330, Springer, 2010.
• [10] J. Majewski, R. Wojtyna. Taking laws out of trained neural networks, IEEE Workshop SPA 2010 (Signal Processing - Algorithms, Architectures, Arrangements and Applications), pp. 21-24, Poznań 2010.