Some notes on perceptron learning

Using a geometrical approach to the perceptron it is shown that, given n examples, learning is of maximal difficulty when the number of inputs, d, is such that n=5d. A modified perceptron algorithm that takes advantage of the pecularities of the cost function is presented. It is more than two times faster than the standard one. It does not have fixed parameters, like the usual learning constant η, but it adapts them to the cost function. It is shown that there exists an optimal choice for β, the steepness of the transfer function. A brief systematic study of the parameters η and β of the standard perceptron algorithm is presented