An Improved Version of the Pseudo-Inverse Solution for Classification and Neural Networks

We present in this letter a noniterative learning rule for classification and neural networks, which allows to eliminate the drawback of overfitting of the pseudo-inverse (PI) solution and to preserve good learning performances. This solution, which is obtained by artificially increasing the number of patterns in the learning set, is a parametric form between the pseudo-inverse and the Hebb solutions. The results are compared to each other and with those of a gradient descent iterative procedure on two very different examples. We show that the proposed solution is near to the one of the iterative procedure.