Multi-view learning (MVL) is an active direction in machine learning that aims at exploiting the consensus and complementarity information among multiple distinct feature sets to boost the generalization performance of the counterpart algorithm. So far, two classical SVM-based MVL methods are SVM-2K and multi-view twin support vector machine (MvTSVM). They are designed only for two-view classification and cannot tackle the general multi-view classification problem. They also cannot effectively leverage the complementarity information among different feature views. In this paper, we propose two novel multi-view support vector machines with the consensus and complementarity information for MVL that not only can deal with the two-view classification problem but also the general multi-view classification problem by jointly learning multiple different views in a non-pairwise way. The disagreement among different views is regarded as a constraint or a regularization term in the objective function which plays an important role in exploring the consensus information. Combination weights for the reconstruction of each view in regularization terms are learned to explore complementarity information among different views. Finally, an efficient iteration algorithm with the classical convex quadratic programming is developed for optimization. Experimental results validate the effectiveness of our proposed methods.

Generalized eigenvalue proximal support vector machines (GEPSVMs) are a simple and effective binary classification method in which each hyperplane is closest to one of the two classes and as far as possible from the other class. They solve a pair of generalized eigenvalue problems to obtain two nonparallel hyperplanes. Multiview learning considers learning with multiple feature sets to improve the learning performance. In this paper, we propose multiview GEPSVMs (MvGSVMs) which effectively combine two views by introducing a multiview co-regularization term to maximize the consensus on distinct views, and skillfully transform a complicated optimization problem to a simple generalized eigenvalue problem. We also propose multiview improved GEPSVMs (MvIGSVMs), which use the minus instead of ratio in MvGSVMs to measure the differences of the distances between the two classes and the hyperplane and lead to a simpler eigenvalue problem. Linear MvGSVMs and MvIGSVMs are generalized to the nonlinear case by the kernel trick. Experimental results on multiple data sets show the effectiveness of our proposed approaches.