  We propose a new method for local distance metric learning based on sample
similarity as side information. These local metrics, which utilize conical
combinations of metric weight matrices, are learned from the pooled spatial
characteristics of the data, as well as the similarity profiles between the
pairs of samples, whose distances are measured. The main objective of our
framework is to yield metrics, such that the resulting distances between
similar samples are small and distances between dissimilar samples are above a
certain threshold. For learning and inference purposes, we describe a
transductive, as well as an inductive algorithm; the former approach naturally
befits our framework, while the latter one is provided in the interest of
faster learning. Experimental results on a collection of classification
problems imply that the new methods may exhibit notable performance advantages
over alternative metric learning approaches that have recently appeared in the
literature.
