\section{KERNELIZED METRIC LEARNING}\label{KernelizedML}
Traditional Mahalanobis distance metric learning is equivalent to learning a linear mapping of the data such that Euclidean distance in the mapped space agrees with a set of labels, such as class labels or triplet comparisons. Often, we are interested in a richer set of mappings than linear ones. Indeed, this is the idea that underlies deep learning and kernel learning. In this section, we provide the first theoretical study of nonlinear metric learning in an RKHS from triplet data, extending the linear results of \cite{mason2017learning}. 
%We begin by carefully demonstrating how to learn a kernelized Mahalanobis metric via convex optimization.






