  This paper is about similarity between objects that can be represented as
points in metric measure spaces. A metric measure space is a metric space that
is also equipped with a measure. For example, a network with distances between
its nodes and weights assigned to its nodes is a metric measure space. Given
points x and y in different metric measure spaces or in the same space, how
similar are they? A well known approach is to consider x and y similar if their
neighborhoods are similar. For metric measure spaces, similarity between
neighborhoods is well captured by the Gromov-Hausdorff-Prokhorov distance, but
it is NP-hard to compute this distance even in quite simple cases. We propose a
tractable alternative: the radial distribution distance between the
neighborhoods of x and y. The similarity measure based on the radial
distribution distance is coarser than the similarity based on the
Gromov-Hausdorff-Prokhorov distance but much easier to compute.
