  High dimensional structured data such as text and images is often poorly
understood and misrepresented in statistical modeling. The standard histogram
representation suffers from high variance and performs poorly in general. We
explore novel connections between statistical translation, heat kernels on
manifolds and graphs, and expected distances. These connections provide a new
framework for unsupervised metric learning for text documents. Experiments
indicate that the resulting distances are generally superior to their more
standard counterparts.
