Performance Analysis of spectral community detection in realistic graph models

Abstract : This article proposes a spectral analysis of dense random graphs generated by (a modified version of) the degree-corrected stochastic block model, for a setting where the inter block probabilities differ by O(n^(−1/2)) with n the number of nodes. We study a normalized version of the graph modularity matrix which is shown to be asymptoti-cally well approximated by an analytically tractable (spiked) random matrix. The analysis of the latter allows for the precise evaluation of (i) the transition phase where clustering becomes asymptotically feasible and (ii) the alignment between the dominant eigenvectors and the block-wise canonical basis, thus enabling the estimation of mis-classification rates (prior to post-processing) in simple scenarios.
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Hafiz Tiomoko Ali, Romain Couillet. Performance Analysis of spectral community detection in realistic graph models. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'16), Shanghai, China, Mar 2016, Shanguai, China. ⟨hal-01322797⟩

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