Fitting a graph to vector data

Abstract

We introduce a measure of how well a combinatorial graph ts a collection of vectors. The optimal graphs under this measure may be computed by solving convex quadratic programs and have many interesting properties. For vectors in d dimensional space, the graphs always have average degree at most 2(d+1), and for vectors in 2 dimensions they are always planar. We compute these graphs for many standard data sets and show that they can be used to obtain good solutions to classifi cation, regression and clustering problems.