Regression-based Metric Learning

In this paper, we present a novel regression-based metric learning (RML) algorithm for solving the regression problems. Most of the metric learning (ML) algorithms can be used to solve the classification problems effectively, but none of them can be used to solve the regression problems. The main reason lies in the increasing difficulty brought by the establishment of the sample constraints for the regression problems. In order to overcome this obstacle, we establish the sample constraints in the objective space of the sample, instead of the feature space. Like most of the ML algorithms, the RML can also be used to reduce data dimensionality. It projects each sample point into a low-rank space through learning a proper Mahalanobis matrix. In addition, the RML can be applied to the arbitrary regression model. Simulation results based on various LICI datasets are provided to demonstrate that the proposed RML approach can obtain better performance.