Why 4D math followed by 7D math rather than just 7D from the beginning?
The main differences are that you have to assign a bin in one case, and then most points are near the center?
The 7D is being computed for everything that 4D is computed for
4D is used to figure out which is the most appropriate cluster
7D refines the radius-1 calculation but never changes the cluster
They have used the 4D data to visualize the clusters and to define them; the others have tight ranges
Research needed to determine the answers for 7D