  In this paper we present two related, kernel-based Distance Metric Learning
(DML) methods. Their respective models non-linearly map data from their
original space to an output space, and subsequent distance measurements are
performed in the output space via a Mahalanobis metric. The dimensionality of
the output space can be directly controlled to facilitate the learning of a
low-rank metric. Both methods allow for simultaneous inference of the
associated metric and the mapping to the output space, which can be used to
visualize the data, when the output space is 2- or 3-dimensional. Experimental
results for a collection of classification tasks illustrate the advantages of
the proposed methods over other traditional and kernel-based DML approaches.
