Using Ripley's K-function to improve graph-based clustering techniques

The success of any graph-based clustering algorithm depends heavily on the quality of the similarity matrix being clustered, which is itself highly dependent on point-wise scaling parameters. We propose a novel technique for finding point-wise scaling parameters based on Ripley's K-function which enables data clustering at different density scales within the same dataset. Additionally, we provide a method for enhancing the spatial similarity matrix by including a density metric between neighborhoods. We show how our proposed methods for building similarity matrices can improve the results attained by traditional approaches for several well known clustering algorithms on a variety of datasets.