A unifying framework in vector-valued reproducing kernel Hilbert spaces for manifold regularization and co-regularized multi-view learning

作     者：Kevin Murphy Bernhard Schölkopf Hà Quang Minh Loris Bazzani Vittorio Murino 

作者机构：Google MPI for Intelligent Systems Pattern Analysis and Computer Vision Istituto Italiano di Tecnologia Genova Italy 

出 版 物：《The Journal of Machine Learning Research》 

年 卷 期：2016年第17卷第1期

学科分类：08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：kernel methods manifold regularization multi-class classification multi-kernel learning multi-modality learning multi-view learning vector-valued RKHS 

摘      要：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 data sets, demonstrate the competitiveness of our algorithms compared with other state-of-the-art methods.