Spectral Clustering from the Discrepancy View and Generalized Quasirandomness

Authors: Marianna Bolla

Abstract:

The aim of this paper is to compare spectral, discrepancy, and degree properties of expanding graph sequences. As we can prove equivalences and implications between them and the definition of the generalized (multiclass) quasirandomness of Lovasz–Sos (2008), they can be regarded as generalized quasirandom properties akin to the equivalent quasirandom properties of the seminal Chung-Graham-Wilson paper (1989) in the one-class scenario. Since these properties are valid for deterministic graph sequences, irrespective of stochastic models, the partial implications also justify for low-dimensional embedding of large-scale graphs and for discrepancy minimizing spectral clustering.

Keywords: generalized random graphs, multiway discrepancy, normalized modularity spectra, spectral clustering