Complexity versus Agreement for Many Views Co-regularization for Multi-view Semi-supervised Learning

The paper considers the problem of semi-supervised multiview 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.