  Metric learning has been successful in learning new metrics adapted to
numerical datasets. However, its development on categorical data still needs
further exploration. In this paper, we propose a method, called CPML for
\emph{categorical projected metric learning}, that tries to efficiently~(i.e.
less computational time and better prediction accuracy) address the problem of
metric learning in categorical data. We make use of the Value Distance Metric
to represent our data and propose new distances based on this representation.
We then show how to efficiently learn new metrics. We also generalize several
previous regularizers through the Schatten $p$-norm and provides a
generalization bound for it that complements the standard generalization bound
for metric learning. Experimental results show that our method provides
