I have spatial data(2D) with some quantity associated with each point - basically 3D data. I want to model the quantity distribution in the space and then use N clusters as a compact representation. My idea is to interpolate with a spline surface over the points, then scale the quantity at each point so that the integral of the spline be equal to 1. How can I find the best approximation of the spline using a weighted sum of N(fixed number) gaussians? I want to use then the means of the gaussians as cluster centers.
PS: Do you think that there is a better approach to the problem?