Optimizing spectral diversity for graph signal coarsening

Graph signal coarsening (GSC) is a kind of dimensionality reduction in irregular domain, where a coarser version of the signal and that of the underlying graph are obtained at the same time. In this paper, we propose spectral diversity for the first time for measuring the similarity between graph signals. The problem of optimizing spectral diversity for graph signal coarsening is studied, showing that the spectrum of the coarsened graph should be a subset of that of the original one. A new GSC method is then proposed, utilizing a greedy method for spectrum selection and an ADMM-based approach for graph signal acquisition. Numerical experiments demonstrate that the proposed method performs better than available reference algorithms.