  In this paper, we present a novel two-stage metric learning algorithm. We
first map each learning instance to a probability distribution by computing its
similarities to a set of fixed anchor points. Then, we define the distance in
the input data space as the Fisher information distance on the associated
statistical manifold. This induces in the input data space a new family of
distance metric with unique properties. Unlike kernelized metric learning, we
do not require the similarity measure to be positive semi-definite. Moreover,
it can also be interpreted as a local metric learning algorithm with well
defined distance approximation. We evaluate its performance on a number of
datasets. It outperforms significantly other metric learning methods and SVM.
