A Unifying Framework in Vector-valued Reproducing Kernel Hilbert Spaces for Manifold Regularization and Co-Regularized Multi-view Learning

摘要

This paper presents a general vector-valued reproducing kernelHilbert spaces (RKHS) framework for the problem of learning anunknown functional dependency between a structured input spaceand a structured output space. Our formulation encompasses bothVector-valued Manifold Regularization and Co-regularized Multi-view Learning, providing in particular a unifying frameworklinking these two important learning approaches. In the case ofthe least square loss function, we provide a closed formsolution, which is obtained by solving a system of linearequations. In the case of Support Vector Machine (SVM)classification, our formulation generalizes in particular boththe binary Laplacian SVM to the multi-class, multi-view settingsand the multi-class Simplex Cone SVM to the semi-supervised,multi-view settings. The solution is obtained by solving asingle quadratic optimization problem, as in standard SVM, viathe Sequential Minimal Optimization (SMO) approach. Empiricalresults obtained on the task of object recognition, usingseveral challenging data sets, demonstrate the competitivenessof our algorithms compared with other state-of-the-art methods. color="gray">