Czasopismo | ELEKTRONIKA - KONSTRUKCJE, TECHNOLOGIE, ZASTOSOWANIA | Rocznik 2011 - zeszyt 5

Special neural networks for finding symbolic relationships between empirical data

nr katalogowy: 59599

Information about objects or phenomena encountered in physical world is sometimes available only in a numerical discrete data form. In such situations, there is often a need to establish symbolic relation between the given empirical data. In addition to other methods, it can be realized by using special-type neural networks. First papers dealing with the neural-network approach to this subject were dedicated to astronomy problems [1.2]. A simple neural implementation of relationships described by so called product units has been proposed in [1] as a way to discover the unknown rules governing the empirical date. This idea has been developed in [2], where the product-unit description function has been expanded to a polynomial expression form given by: (1) The equation (1) enables to extend the class of problems that can be described in a symbolic way. When implementing (1) in a special-neural-network form shown in Fig. 1, the symbols in (1) take the following meaning: y is the network output signal, xj are components of its input vector, wij represent power to which xj is raised, n is a number of the xj input components and h the number of neurons included in the hidden layer. The solution shown in Fig. 1 is a special type neural network because as activation operators the exp(.) and ln(.) functions were introduced into proper places, i.e. into the input nodes and hidden layer. Comparing the scheme of Fig. 1 with the middle part of the expression (1) we see that this is really a neural realization of (1). ĄŇ ĄŇ ( ) ĄŇ ĄĐ = = = = + = ˙ ˙ . . . . . . = + h i n j w i j n j ij j h i i y c c w x c c x ij 1 1 0 1 1 0 exp ln , In this paper, we go further and propose to enlarge the group of product-unit and polynomial expressions by adding to it functions of a fractional rational type. As we know, such functions can be presented as ratio of two polynomials which in case of only one independent variable, x, [...]

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