A basic problem in classifying, or searching for similar objects, in a large set of geometric objects is computing similarity between two objects. There has been extensive work on computing geometric similarity between two objects. In many application, it is not sufficient to return a single similarity score. Instead, a map between two objects that identifies shared structures is needed.

This talk discusses some recent work on computing maps between two or more objects. The talk consists of two parts. The first part is devoted to computing maps between a pair of trajectories and clustering similar portions of trajectories. The second part focuses on computing maps between two weighted point sets, say, distributions.