Abstract
This paper investigates an online gradient method with inner- penalty for a novel feed forward network it is called pi-sigma network. This network utilizes product cells as the output units to indirectly incorporate the capabilities of higher-order networks while using a fewer number of weights and processing units. Penalty term methods have been widely used to improve the generalization performance of feed forward neural networks and to control the magnitude of the network weights. The monotonicity of the error function and weight boundedness with inner- penalty term and both weak and strong convergence theorems in the training iteration are proved.
Highlights
A novel higher order feedforward polynomial neural network is known to provide inherently more powerful mapping abilities than traditional feed forward neural network called the pi-sigma network (PSN) [2]. This network utilizes product cells as the output units to indirectly incorporate the capabilities of higher-order networks while using a fewer number of weights and processing units
The neural networks consisting of the PSN modules has been used effectively in pattern classification and approximation problems [1, 4, 10, 11].There are two ways of training to updating weight: The first approach, batch training[18],the weights are modified after each training pattern is presented to the network
The penalty term is often introduced into the network training algorithms has been widely used so as to control the magnitude of the weights and to improve the generalization performance of the network [6, 8], here the generalization performance refers to the capacity of a neural network to give correct outputs for untrained data
Summary
A novel higher order feedforward polynomial neural network is known to provide inherently more powerful mapping abilities than traditional feed forward neural network called the pi-sigma network (PSN) [2]. This network utilizes product cells as the output units to indirectly incorporate the capabilities of higher-order networks while using a fewer number of weights and processing units. Mohamed et al.: Convergence of Online Gradient Method for Pi-sigma Neural Networks with Inner-penalty Terms improve the generalization performance of the network [5, 9, 17].
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