Complexity Versus Agreement for Many Views

Abstract

The paper considers the problem of semi-supervised multi-view classification, where each view corresponds to a Reproducing Kernel Hilbert Space. An algorithm based on co-regularization methods with extra penalty terms reflecting smoothness and general agreement properties is proposed. We first provide explicit tight control on the Rademacher ( L _1) complexity of the corresponding class of learners for arbitrary many views, then give the asymptotic behavior of the bounds when the co-regularization term increases, making explicit the relation between consistency of the views and reduction of the search space. Since many views involve many parameters, we third provide a parameter selection procedure, based on the stability approach with clustering and localization arguments. To this aim, we give an explicit bound on the variance ( L _2-diameter) of the class of functions. Finally we illustrate the algorithm through simulations on toy examples.