For a project I'm working on, I have two sets of samples, where each set has N x length 7 vectors. For context, each vector represents the joint parameter setting for a robot (the angle each joint of the robot is set to).
I'm interested in comparing the similarity of the distributions from which the vectors were drawn from. I understand typically you can use KL-Divergence/MMD/etc., but these methods aren't appropriate (I don't think at least) because of the circular topology of the data - I.e. the value 0 and 2pi are the same, but would be considered far apart by a standard similarity measure for probability distributions.
How can I calculate a numeric similarity between the two distributions from which the samples were drawn from given this circular topology?
brief extra: An idea I had was to convert each angle into a (x, y) pair, $\theta \rightarrow (cos(\theta), sin(\theta))$. Then the problem becomes comparing the distributions of vectors of (x,y) pairs, not sure that thats a great path to head down though