One Dimensional Cross-Correlation Methods For Deterministic And Stochastic Graph Signals With A Twitter Application In Julia

Graph signal processing is increasingly becoming important for discovering latent patterns, primarily higher order ones, in massive, linked, and possibly semistructured data. The latter may well include social networks, digital images, music spectrograms, brain connectivity maps, protein-to-protein interaction graphs, and even event dependency graphs between events from standard probability spaces. Computing efficiently the cross-correlation between two graph signals can be a versatile similarity metric between them, paving the way for distance metrics in graph clustering or graph classification tasks in numerous domains. In this conference paper methods from a broad class of cross-correlation methodologies which convert deterministic graphs to one dimensional signals are examined. This analysis is then extended to a class of random graphs with the latter being treated as stochastic signals. As a concrete application, these approaches are applied to benchmark data consisting respectively of Twitter connectivity graphs and instances of synthetic stochastic ones.