We present a distance metric learning algorithm for regression problems, which incorporates label information to form a biased distance metric in the process of learning. We use Newton's optimization method to solve an optimization problem for the sake of learning this biased distance metric. Experiments show that this method can find the intrinsic variation trend of data in a regression model by a relative small amount of samples without any prior assumption of the structure or distribution of data. In addition, the test sample data can be projected to this metric by a simple linear transformation and it is easy to be combined with manifold learning algorithms to improve the performance. Experiments are conducted on the FG-NET aging database, the UIUC-IFP-Y aging database, and the CHIL head pose database by Gaussian process regression based on the learned metric, which shows that our method is competitive among the start-of-art.
