Learning Riemannian Metrics
  We propose a solution to the problem of estimating a Riemannian metric associated with a given differentiable manifold. The metric learning problem is based on minimizing the relative volume of a given set of points. We derive the details for a family of metrics on the multinomial simplex. The resulting metric has applications in text classification and bears some similarity to TFIDF representation of text documents. 
Guy Lebanon
cs.LG stat.ML