I was thinking of the following problem: Imagine I am given two lists of points on a 2D plane. These lists have the same size, i.e. both lists have the same number of points.
Now, I want to be able to compare these two patterns of points. How could I do that mathematically/statistically?
I calculated the distance (Euclidean) from each point to every other point (pairwise distance). Then, I've ordered these distances. After that, I pick the first pair which will be the distance between two points a and b. At this point, I will ignore any other distance containing a or b (if a is in the first pattern and b in the second pattern). Thus at the end I will have a "matching" that creates a minimum weight match.
Finally, I just sum up these distances and this is my distance coefficient.
Any other ideas?
An example Suppose I have: $[ (0,0), (0,1), (1,0), (1,1)]$ and $[(0,0), (2,1), (0,1), (1,0)]$ and $[(2,3), (2,0), (0,0), (0,2)]$
How similar are they? Which are the most similar pairs? I want to answer questions like these.