Recursive algorithms for pattern classification using misclassified samples

We consider the samples x(i) belonging to one of the two non-overlapping classes, ω1 and ω0, 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))]η(i) where η(i) is the measurement noise and E(η) 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).