Suppose I'm given many GMMs. All have $K$ components. My goal is to find a GMM with $K$ components that can best represent the given GMMs. It is like finding the center of many points but a point here is a GMM.
So my first question is: are there any ways to find the "center" in closed form?
My current solution, maybe not the easiest one, is to first find a distance measure between GMMs and then find a GMM that has the smallest overall distance to the given GMMs. Both the distance and the closest GMM should be computed in closed form.
This answer gives three distance measures between two GMMs that are available in closed form. I haven't tried to find out whether the closest GMM could also be computed in closed form. But before I do that, I want to ask my second question:
Since all the GMMs have the same number of components, which is a special case. Are there any other distances that also available in closed form?
Thanks!
