Learning with box kernels

Supervised examples and prior knowledge expressed by propositions have been profitably integrated in kernel machines so as to improve the performance of classifiers in different real-world contexts. In this paper, using arguments from variational calculus, a novel representer theorem is proposed which solves optimally a more general form of the associated regularization problem. In particular, it is shown that the solution is based on box kernels, which arises from combining classic kernels with the constraints expressed in terms of propositions. The effectiveness of this new representation is evaluated on real-world problems of medical diagnosis and image categorization.