Pretopological approach for supervised learning

This article presents a pretopological approach for supervised learning, suited for the recognition of printed characters. This approach is an alternative to classic methods that use the “nearest neighbors rules” (NNR). We define a particular neighborhood which authorizes an optimal recovery of the training set in order to reduce the complexity of calculations during the recognition process. The number of neighborhoods does not depend on the size of training set but depend rather on the classes complexity. The degree of modelization wished is fixed by a parameter. For extreme values of this parameter, classes limits are near those deduced by the 1-NNR. This approach also allows to estimate the a priori substitution rate for each class and gives a good evaluation of the classes separability