Prior Knowledge and the Creation of \virtual" Examples for Rbf Networks 1

We consider the problem of how to incorporate prior knowledge in supervised learning techniques. We set the problem in the framework of regularization theory, and consider the case in which we know that the approximated function has radial symmetry. The problem can be solved in two alternative ways: 1) use the invariance as a constraint in the regulariza-tion theory framework to derive a rotation invariant version of Radial Basis Functions; 2) use the radial symmetry to create new, \virtual" examples from a given data set. We show that these two apparently diierent methods of learning from \hints" (Abu-Mostafa, 1993) lead to exactly the same analytical solution.