Consistency of spectral clustering in stochastic block models
This provides a theoretical guarantee for spectral clustering in network analysis, which is incremental but important for applications like social network analysis.
The paper tackles the problem of community recovery in stochastic block models using spectral clustering, showing that it can consistently recover hidden communities even when the maximum expected degree is as small as log n, where n is the number of nodes.
We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as $\log n$, with $n$ the number of nodes. This result applies to some popular polynomial time spectral clustering algorithms and is further extended to degree corrected stochastic block models using a spherical $k$-median spectral clustering method. A key component of our analysis is a combinatorial bound on the spectrum of binary random matrices, which is sharper than the conventional matrix Bernstein inequality and may be of independent interest.