Robust Distance Metric Learning via Bayesian Inference.

Distance metric learning (DML) has achieved great success in many computer vision tasks. However, most existing DML algorithms are based on point estimation, and thus are sensitive to the choice of training examples and tend to be over-fitting in the presence of label noise. In this paper, we present a robust DML algorithm based on Bayesian inference. In particular, our method is essentially a Bayesian extension to a previous classic DML method-large margin nearest neighbor classification and we use stochastic variational inference to estimate the posterior distribution of the transformation matrix. Furthermore, we theoretically show that the proposed algorithm is robust against label noise in the sense that an arbitrary point with label noise has bounded influence on the learnt model. With some reasonable assumptions, we derive a generalization error bound of this method in the presence of label noise. We also show that the DML hypothesis class in which our model lies is probably approximately correct-learnable and give the sample complexity. The effectiveness of the proposed method is demonstrated with state of the art performance on three popular data sets with different types of label noise. A MATLAB implementation of this method is made available at http://parnec.nuaa.edu.cn/xtan/Publication.htm.