  Metrics specifying distances between data points can be learned in a
discriminative manner or from generative models. In this paper, we show how to
unify generative and discriminative learning of metrics via a kernel learning
framework. Specifically, we learn local metrics optimized from parametric
generative models. These are then used as base kernels to construct a global
kernel that minimizes a discriminative training criterion. We consider both
linear and nonlinear combinations of local metric kernels. Our empirical
results show that these combinations significantly improve performance on
classification tasks. The proposed learning algorithm is also very efficient,
achieving order of magnitude speedup in training time compared to previous
discriminative baseline methods.
