Multi-view ordinal regression with feature augmentation and privileged information learning

Abstract

Ordinal regression deals with the classification problems that the classes are ranked in order. The majority of existing ordinal regression approaches are designed for single-view data, and only a little work is done on multi-view ordinal regression. However, these multi-view ordinal regression works mainly concentrate on the consensus information between different views, while the complementary information that is critical in multi-view learning is not adequately considered in learning the ordinal regression classifier. In this paper, we put forward the multi-view ordinal regression model that incorporates feature augmentation and privileged information learning (MORFP). Firstly, distinguished from the existing multi-view ordinal regression approaches that mainly embody the consensus principle, MORFP introduces the concept of privileged information learning and implements both the consensus and complementarity principles. Based on the concept of privileged information learning, we treat one view as the privileged information of another view, so that different views can supply complementary information to enhance each other. Secondly, considering that the distributions of data in distinct views may be are greatly different, we map those views to a common subspace and augment this subspace by incorporating the original features of each view. By combining the original features in the views and projected features in the common subspace, the learned ordinal regression classifier is expected to have better discriminative ability than that learned on only the projected features or the original features. Lastly, we employ a heuristic framework to resolve the learning problem of MORFP, which trains the multi-view ordinal regression classifier and optimizes the projection matrices alternately. Numerical studies on real-life datasets have demonstrated that MORFP performs explicitly better than the existing multi-view ordinal regression approaches.