Power to the points: validating data memberships in clusterings

In this paper, we present a method to attach affinity scores to the implicit labels of individual points in a clustering. The affinity scores capture the confidence level of the cluster that claims to "own" the point. We demonstrate that these scores accurately capture the quality of the label assigned to the point. We also show further applications of these scores to estimate global measures of clustering quality, as well as accelerate clustering algorithms by orders of magnitude using active selection based on affinity. This method is very general and applies to clusterings derived from any geometric source. It lends itself to easy visualization and can prove useful as part of an interactive visual analytics framework. It is also efficient: assigning an affinity score to a point depends only polynomially on the number of clusters and is independent both of the size and dimensionality of the data. It is based on techniques from the theory of interpolation, coupled with sampling and estimation algorithms from high dimensional computational geometry.