SIMULATION OF OBJECTIVE FUNCTION FOR TRAINING OF NEW HIDDEN UNITS IN CONSTRUCTIVE NEURAL NETWORKS

ABSTRACT

The present research article represent the mathematical analysis of objective function for training new hidden units in constructive algorithms for multi-layer feed-forward networks. Neural re-search, now days, is highly attractive wing under research community which may lead the development of some hidden prospects by using mathematical modeling which involve the design of neurons network. The network size is highly important for neural network. Small network as well as large network size cannot be learned very well, but there is an optimum size for which the neural network can be involved for good results. Constructive algorithms started with a small network size and then grow additional hidden units until a satisfactory solution is found. A network, having n-1 hidden units, is directly connected to the n-1 output unit, which is modeled as  and is the residual error function for j=i current network with n —1 hidden units. A new hidden unit is added under a process in input as a linear combination of g_n with the current network f_n-1 + _n  which governed the minimum residual error  in the output process by keeping  fixed and adjusted value of _n so as to minimize residual error. The function to be optimized during input training is  and corresponding objective function is where H_p is the activation function of the new hidden unit and E_p is the corresponding residual error before this new hidden unit is added.

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