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Neural networks suitable for law discovery tasks

Majewski J., Wojtyna R.

Image Processing & Communications

2010

Vol. 15, no 2

17-25

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.