Abstract

We propose a novel approach to clustering, based on deterministic analysis of random walks on the weighted graph associated with the clustering problem. The method is centered around what we shall call \emph{separating operators}, which are applied repeatedly to sharpen the distinction between the weights of inter-cluster edges (the so-called separators), and those of intra-cluster edges. These operators can be used as a stand-alone for some problems, but become particularly powerful when embedded in a classical multi-scale framework and/or enhanced by other known techniques, such as agglomerative clustering. The resulting algorithms are simple, fast and general, and appear to have many useful applications.

Citations