  Distance metric learning is an important component for many tasks, such as
statistical classification and content-based image retrieval. Existing
approaches for learning distance metrics from pairwise constraints typically
suffer from two major problems. First, most algorithms only offer point
estimation of the distance metric and can therefore be unreliable when the
number of training examples is small. Second, since these algorithms generally
select their training examples at random, they can be inefficient if labeling
effort is limited. This paper presents a Bayesian framework for distance metric
learning that estimates a posterior distribution for the distance metric from
labeled pairwise constraints. We describe an efficient algorithm based on the
variational method for the proposed Bayesian approach. Furthermore, we apply
the proposed Bayesian framework to active distance metric learning by selecting
those unlabeled example pairs with the greatest uncertainty in relative
distance. Experiments in classification demonstrate that the proposed framework
achieves higher classification accuracy and identifies more informative
training examples than the non-Bayesian approach and state-of-the-art distance
metric learning algorithms.
