  We revisit the task of learning a Euclidean metric from data. We approach
this problem from first principles and formulate it as a surprisingly simple
optimization problem. Indeed, our formulation even admits a closed form
solution. This solution possesses several very attractive properties: (i) an
innate geometric appeal through the Riemannian geometry of positive definite
matrices; (ii) ease of interpretability; and (iii) computational speed several
orders of magnitude faster than the widely used LMNN and ITML methods.
Furthermore, on standard benchmark datasets, our closed-form solution
consistently attains higher classification accuracy.
