Recursive algorithms for pattern classification using misclassified samples

We consider the samples x(i) belonging to one of the two non-overlapping classes, ??1 and ??0, which possess a separating function f(x). The observed membership of pattern x(i) is represented by the variable z(i) which can assume only one of two values, ?? 1, or z(i) = [sgn f(x(i))]??(i) where ??(i) is the measurement noise and E(??) is known. Thus the membership of the training samples may be erroneous. Using only the available sample pairs {x(i),z(i)}, i=1,2,..., we will obtain either a separating function or an optimal approximation to the separating function f(x).