  This paper presents a general vector-valued reproducing kernel Hilbert spaces
(RKHS) framework for the problem of learning an unknown functional dependency
between a structured input space and a structured output space. Our formulation
encompasses both Vector-valued Manifold Regularization and Co-regularized
Multi-view Learning, providing in particular a unifying framework linking these
two important learning approaches. In the case of the least square loss
function, we provide a closed form solution, which is obtained by solving a
system of linear equations. In the case of Support Vector Machine (SVM)
classification, our formulation generalizes in particular both the binary
Laplacian SVM to the multi-class, multi-view settings and the multi-class
Simplex Cone SVM to the semi-supervised, multi-view settings. The solution is
obtained by solving a single quadratic optimization problem, as in standard
SVM, via the Sequential Minimal Optimization (SMO) approach. Empirical results
obtained on the task of object recognition, using several challenging datasets,
demonstrate the competitiveness of our algorithms compared with other
state-of-the-art methods.
