Seminal Contributions to Modelling and Simulation by Khalid Al-Begain & Andrzej Bargiela

Author:Khalid Al-Begain & Andrzej Bargiela
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

9.1.2 Pseudo Neural Networks

The interest about classification by means of some automatic process has been enlarged with the development of artificial neural networks (ANN). They can be used also for a lot of other possible applications like pattern recognition, prediction, control, signal filtering, approximation, etc. All artificial neural networks are based on some relation between inputs and output(s), which utilizes mathematical transfer functions and optimized weights from training process. The setting-up of layers, number of neurons in layers, estimating of suitable values of weights is a demanding procedure. On account of this fact, pseudo neural networks, which represent the novelty approach using symbolic regression with evolutionary computation, is proposed in this paper.

Symbolic regression in the context of evolutionary computation means to build a complex formula from basic operators defined by users. The basic case represents a process in which the measured data is fitted and a suitable mathematical formula is obtained in an analytical way. This process is widely known for mathematicians. They use this process when a need arises for mathematical model of unknown data, i.e. relation between input and output values. The proposed technique is similar to synthesis of analytical form of mathematical model between input and output(s) in training set used in neural networks. Therefore, it is called Pseudo Neural Networks .

Initially, John Koza proposed the idea of symbolic regression done by means of a computer in Genetic Programming (GP) [1, 16, 17]. The other approaches are e.g. Grammatical Evolution (GE) developed by Conor Ryan [23] and here described Analytic Programming [25, 39, 40].

The above-described tools were recently commonly used for synthesis of artificial neural networks but in a different manner than is presented here. One possibility is the usage of evolutionary algorithms for optimization of weights to obtain the ANN training process with a small or no training error result. Some other approaches represent the special ways of encoding the structure of the ANN either into the individuals of evolutionary algorithms or into the tools like Genetic Programming. But all of these methods are still working with the classical terminology and separation of ANN to neurons and their transfer functions [7]. In this paper, the proposed technique synthesizes the structure without a prior knowledge of transfer functions and inner potentials. It synthesizes the relation between inputs and output of training set items used in neural networks so that the items of each group are correctly classified according the rules for cost function value. The data set used for training is Iris data set (Machine Learning Repository [8, 20]). It is a very well-known benchmark data set for classification problem, which was introduced by Fisher for the first time.

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