A Maximum Entropy approach to Massive Graph Spectra
This addresses the need for robust and scalable spectral methods in graph analysis, offering a principled solution for researchers and practitioners working with large networks, though it is incremental in improving existing techniques.
The paper tackles the problem of ad-hoc kernel selection in graph spectral techniques for similarity and clustering by proving that kernel smoothing biases spectral density moments, and proposes an information-theoretically optimal method that respects moment information and scales linearly with edges, outperforming iterative spectral approaches on synthetic and real graphs.
Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting output. We prove that kernel smoothing biases the moments of the spectral density. We propose an information theoretically optimal approach to learn a smooth graph spectral density, which fully respects the moment information. Our method's computational cost is linear in the number of edges, and hence can be applied to large networks, with millions of nodes. We apply our method to the problems to graph similarity and cluster number learning, where we outperform comparable iterative spectral approaches on synthetic and real graphs.