Law discovery perceptrons and way of their learning

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

Abstrakty

EN

The problem of utilizing atypical neural networks to create a symbolic description of rules governing a set of empirical data is considered. We propose to use fractional–rational or polynomial functions as a versatile tool to describe the unknown empirical–data rules. Our aim is to transform basic forms of these functions to others, suitable for neural implementations, i.e. by means of special–type perceptrons capable of determining the function coefficients in a way of learning the perceptrons. We discuss the issue of effective learning such networks. Important elements in improving the learning efficiency are: a) performing some transformations of the fractional–rational or polynomial functions; b) introducing some additional parameters into them; c) realizing a complex–valued training. These steps enable to eliminate numerical operations on complex numbers from the learning procedure despite the fact that some parameters of the functions are complex–valued ones and are varied in the learning process. Moreover, the made steps lead to eliminating from the training process time consuming operations like using activation functions of the ln(.) and exp(.) type. The proposed approach has proved to be a successful way to increase the learning speed and improve its robustness. We show how the transformations and the additional parameters can be applied to modify one–dimensional fractional–rational as well as one–dimensional polynomial expressions. Perceptron schemes resulting from the obtained expressions are also presented. Furthermore, we discuss properties of the applied learning method and demonstrate the learning effects.

Słowa kluczowe

EN

complex–valued neural networks; perceptron training; rules governing numerical data; symbolic description methods

PL

sieci neuronowe o wartościach zespolonych; trening perceptronu; zarządzanie danymi numerycznymi; opis symboliczny

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Journal of Applied Computer Science
• Rocznik: 2013
• Tom: Vol. 21, nr 1
• Strony: 71--87
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Majewski J

• University of Technology and Life Sciences, Faculty of Telecommunication and Electrical Engineering, ul. Kaliskiego 7, 85-796 Bydgoszcz, Poland

autor

Wojtyna R.

• University of Computer Sciences and Skills, Bydgoszcz Department, ul. Fordońska 246, 85-959 Bydgoszcz, Poland

Bibliografia

• [1] Durbin, R. and Rumelhart, D., Product Units: A Computationally Powerful and Biologically Plausible Extension to Backpropagation Networks, Neural Computation, Vol. 1, 1989, pp. 133–142.
• [2] Saito, K. and Nakano, R., Discovery of Relevant Weights by Minimizing Cross– Validation Error, In: 4th Pacific–Asia Conference on Knowledge Discovery and Data Mining (PAKDD2000), 2000, pp. 372–375.
• [3] Nakano, R. and Saito, K., Discovery of Nominally Conditioned Polynomials using Neural Networks, Vector Quantizers and Decision Trees, Lecture Notes in Computer Science, Springer–Verlag, Vol. 1967 / 2000, 2000, pp. 325–329.
• [4] Saito, K. and Nakano, R., Law Discovery Using Neural Networks, In: Proc. of the 15th International Joint Conference on Artificial Intelligence, 1997, pp. 1078–1083.
• [5] Washio, T., Motoda, H., and Niwa, Y., Discovering Admissible Simultaneous Equation Models from Observed Data, LNCS 2167, Springer–Verlag, Berlin Heidelberg, 2001, pp. 539–551.
• [6] Majewski, J. and Wojtyna, R., Special neural networks for finding symbolic relationships between numerical data, Elektronika No. 5/2011.
• [7] Majewski, J. and Wojtyna, R., Implementing polynomial expressions by means of reciprocal-function-based neural networks, In: IEEE Workshop Signal Processing – Algorithms, Architectures, Arrangements and Applications (SPA), 2011, pp. 22–26.
• [8] Apostolopoulou, M. S., Sotiropoulos, D. G., Livieris, I. E., and Pintelas, P., A Memoryless BFGS Neural Network Training Algorithm, In: 7th IEEE International Conference on Industrial Informatics (INDIN), 2009, pp. 216–221.
• [9] Majewski, J. and Wojtyna, R., Taking laws out of trained neural networks, In: IEEE Workshop Signal Processing – Algorithms, Architectures, Arrangements and Applications (SPA), 2010, pp. 21–24.