Pairwise Relations Oriented Discriminative Regression

Linear Regression (LR) is a popular and effective technique in pattern recognition area, which aims to find a transform matrix between source data and target data (usually label matrix). However, a binary zero-one label matrix may be too strict and inappropriate for regression. Besides, directly projecting source data to target data by one transform matrix may lose some intrinsic data information. To address these issues, this paper proposes a novel Pairwise Relations oriented Discriminative Regression (PRDR) method. In PRDR, the source data is regressed into a latent space instead of label space. To supervise the discriminative projection learning, the pairwise relations in source data space and label space are exploited in the latent space simultaneously. The pairwise label relations are transferred into the latent subspace by solving a distance-distance difference minimization problem, and the intraclass instance relations are also preserved in latent space. These two constraints ensure the pairwise similarity of data points after transformation which is beneficial for classification. By further enlarging the margins between true and false classes, PRDR is extended to a robust version, i.e., R-PRDR. An efficient algorithm is presented to solve the PRDR model. Extensive experiments on several popular image datasets demonstrate the effectiveness and efficiency of the proposed method compared with some state-of-the-art regression approaches.