Hearing the clusters in a graph: A distributed algorithm

We propose a novel distributed algorithm to decompose graphs or cluster data. The algorithm recovers the solution obtained from spectral clustering without need for expensive eigenvalue/ eigenvector computations. We demonstrate that by solving the wave equation on the graph, every node can assign itself to a cluster by performing a local fast Fourier transform. We prove the equivalence of our algorithm to spectral clustering, derive convergence rates and demonstrate it on examples.