Point Set Similarity Metrics

I am looking for some quick metrics to take to measure the similarity between two sets of points, such as distance between centroids, amount of overlap etc

I would ideally like to take a few more metrics to improve the accuracy of the basic similarity measurements, but the key feature is that they ideally need to开发者_Go百科 be fast and scalable.

Not knowing the application, similarity could mean anything.

• The number of points.
• The dimension of the points.
• The average, variances, and covariances of the coordinates.
• The position, volume, or orientation of a bounding box of type ...
• The radius and position of a smallest enclosing ball.
• The volume and ... of the convex hull.
• The ... of clusters of kind ...
• The density of points in ...
• The ... of ...
• ...

There is probably a real-world reason R why a set of points P are distributed in a certain way. So try to deduce R, and compare the R's for similarity instead.