Coarsening graph signal with spectral invariance

Signal processing on graphs is an emerging field that attracts increasing attention. For applications such as multiscale transforms on graphs, it is often necessary to get a coarsened version of graph signal with its underlying graph. However, most of the existing methods use only topology information but no property of graph signals to complete the process. In this paper, we propose a novel graph signal coarsening method with spectral invariance, which means both the spectrum of the graph and the spectrum of the graph signal are approximately kept invariant. The problem is formulated into an optimization problem and is solved by projected subgradient method. Experiment results verify the effectiveness of the coarsening method.