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 by spectral clustering without using expensive eigenvalue/eigenvector computations or making approximations associated with random walk based approaches. 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, orders of magnitude faster than state of the art distributed clustering algorithms. We prove the equivalence of our algorithm to spectral clustering, derive convergence rates and demonstrate it on examples.