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 kernel Hilbert spaces(RKHS) framework for the problem of learning an unknown functional dependencybetween a structured input space and a structured output space. Our formulationencompasses both Vector-valued Manifold Regularization and Co-regularizedMulti-view Learning, providing in particular a unifying framework linking thesetwo important learning approaches. In the case of the least square lossfunction, we provide a closed form solution, which is obtained by solving asystem of linear equations. In the case of Support Vector Machine (SVM)classification, our formulation generalizes in particular both the binaryLaplacian SVM to the multi-class, multi-view settings and the multi-classSimplex Cone SVM to the semi-supervised, multi-view settings. The solution isobtained by solving a single quadratic optimization problem, as in standardSVM, via the Sequential Minimal Optimization (SMO) approach. Empirical resultsobtained on the task of object recognition, using several challenging datasets,demonstrate the competitiveness of our algorithms compared with otherstate-of-the-art methods.