Achieving compatible numeral handwriting recognition rate by a simple activation function

Most of the supervised neural networks for numeral handwriting recognition employ the sigmoidal activation function to generate the outputs. Although this function performs rather well, its computational time as well as its hardware realization is costly and complicated. Here, we introduce a simple activation function in forms of a recursive piecewise polynomial function as an activation function. The accuracy of recognition can be adjusted according to the parameters of the function. In addition a new risk function measuring the discrepancy between the correct and estimated classification of the network is also presented to improve the performance. The proposed activation function and the risk function can achieve the same accuracy compatible with that from the sigmoidal function when tested with the benchmark data set.