I have a set of n-dimensional points. I am performing clustering analysis on them to partition them into groups. Now, I would like to find a basis set to be able to describe the layout of the groups' borders.
For example, if my points were only three dimensional, then I could easily use spherical harmonics to describe the groups. If there are, say, five groups then each group can be written as a linear combination of spherical harmonics, and I can easily define the borders of each group.
I cannot, however, use spherical harmonics on, for example, a five dimensional set of points, can I? If not, is there a family of basis sets that can define shapes in n-dimensions?