WASD Algorithm with Pruning-While-Growing and Twice-Pruning Techniques for Multi-Input Euler Polynomial Neural Network

Differing from the conventional back-propagation (BP) neural networks, a novel multi-input Euler polynomial neural network, in short, MIEPNN (specifically, 4-input Euler polynomial neural network, 4IEPNN) is established and investigated in this paper. In order to achieve satisfactory performance of the established MIEPNN, a weights and structure determination (WASD) algorithm with pruning-while-growing (PWG) and twice-pruning (TP) techniques is built up for the established MIEPNN. By employing the weights direct determination (WDD) method, the WASD algorithm not only determines the optimal connecting weights between hidden layer and output layer directly, but also obtains the optimal number of hidden-layer neurons. Specifically, a sub-optimal structure is obtained via the PWG technique, then the redundant hidden-layer neurons are further pruned via the TP technique. Consequently, the optimal structure of the MIEPNN is obtained. To provide a reasonable choice in practice, several different MATLAB computing routines related to the WDD method are studied. Comparative numerical-experiment results of the 4IEPNN using these different MATLAB computing routines and the standard multi-layer perceptron (MLP) neural network further verify the superior performance and efficacy of the proposed MIEPNN equipped with the WASD algorithm including PWG and TP techniques in terms of training, testing and predicting.

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