  Metric and kernel learning are important in several machine learning
applications. However, most existing metric learning algorithms are limited to
learning metrics over low-dimensional data, while existing kernel learning
algorithms are often limited to the transductive setting and do not generalize
to new data points. In this paper, we study metric learning as a problem of
learning a linear transformation of the input data. We show that for
high-dimensional data, a particular framework for learning a linear
transformation of the data based on the LogDet divergence can be efficiently
kernelized to learn a metric (or equivalently, a kernel function) over an
arbitrarily high dimensional space. We further demonstrate that a wide class of
convex loss functions for learning linear transformations can similarly be
kernelized, thereby considerably expanding the potential applications of metric
learning. We demonstrate our learning approach by applying it to large-scale
real world problems in computer vision and text mining.
