A Unifying Framework in Vector-valued Reproducing Kernel Hilbert Spaces for Manifold Regularization and Co-Regularized Multi-view Learning
Journal of Machine Learning Research - JMLR
Department of Computer Science
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.
Dartmouth Digital Commons Citation
Minh, Hà Quang; Bazzani, Loris; and Murino, Vittorio, "A Unifying Framework in Vector-valued Reproducing Kernel Hilbert Spaces for Manifold Regularization and Co-Regularized Multi-view Learning" (2016). Dartmouth Scholarship. 2517.