Bayesian Neighborhood Component Analysis.

Learning a distance metric in feature space potentially improves the performance of the nearest neighbor classifier and is useful in many real-world applications. Many metric learning (ML) algorithms are, however, based on the point estimation of a quadratic optimization problem, which is time-consuming, susceptible to overfitting, and lacks a natural mechanism to reason with parameter uncertainty-a property useful especially when the training set is small and/or noisy. To deal with these issues, we present a novel Bayesian ML (BML) method, called Bayesian neighborhood component analysis (NCA), based on the well-known NCA method, in which the metric posterior is characterized by the local label consistency constraints of observations, encoded with a similarity graph instead of independent pairwise constraints. For efficient Bayesian inference, we explore the variational lower bound over the log-likelihood of the original NCA objective. Experiments on several publicly available data sets demonstrate that the proposed method is able to learn robust metric measures from small size data set and/or from challenging training set with labels contaminated by errors. The proposed method is also shown to outperform a previous pairwise constrained BML method.