Document Type

Article

Publication Date

4-16-2016

Publication Title

Journal of Machine Learning Research - JMLR

Department

Department of Computer Science

Abstract

This paper presents a general vector-valued reproducing kernel Hilbert spaces (RKHS) framework for the problem of learning an unknown functional dependency between a struc- tured 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 op- timization problem, as in standard SVM, via the Sequential Minimal Optimization (SMO) approach. Empirical results obtained on the task of object recognition, using several chal- lenging data sets, demonstrate the competitiveness of our algorithms compared with other state-of-the-art methods.

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