Robust multi-view learning with the bounded LINEX loss

Multi-view learning, as a promising direction, emphasizes the consensus principle and the complementarity principle to boost the performance. By exploiting view-consistency or view-discrepancy among different views, numerous successful multi-view support vector machine models have been proposed. However, existing methods face two challenges. Firstly, most multi-view support vector machine models only consider the consensus principle, but ignore the complementarity principle. How to build a novel model with both principles has not been fully considered. Secondly, most multi-view support vector machine models neglect the robustness when the multi-view dataset is contaminated by the noisy samples, error-prone samples and view-inconsistent samples. Considering that the bounded linear-exponential (BLINEX) loss function possesses elegant merits, i.e., asymmetry and boundedness, developing a robust BLINEX-based model is worth exploring. Therefore, in this paper, we propose a BLINEX-based multi-view learning method called MVASY-BX, which explores the consensus and complementarity information with a between-view co-regularization term and importance weights of two views respectively. The mixed BLINEX loss is designed to make the model robust to noisy samples, view-inconsistent samples and error-prone samples. We solve linear and nonlinear MVASY-BX through the stochastic sub-gradient descent algorithm and the alternating direction method of multipliers respectively. Furthermore, we analyze the generalization error bound via Rademacher complexity. The comprehensive experiments confirm that our proposed model is more competitive than other benchmark methods.