Krylov Subspace Approximation for Local Community Detection in Large Networks

Community detection is an important information mining task to uncover modular structures in large networks. For increasingly common large network data sets, global community detection is prohibitively expensive, and attention has shifted to methods that mine local communities, i.e. identifying all latent members of a particular community from a few labeled seed members. To address such semi-supervised mining task, we systematically develop a local spectral subspace-based community detection method, called LOSP. We define a family of local spectral subspaces based on Krylov subspaces, and seek a sparse indicator for the target community via an $\ell_1$ norm minimization over the Krylov subspace. Variants of LOSP depend on type of random walks with different diffusion speeds, type of random walks, dimension of the local spectral subspace and step of diffusions. The effectiveness of the proposed LOSP approach is theoretically analyzed based on Rayleigh quotients, and it is experimentally verified on a wide variety of real-world networks across social, production and biological domains, as well as on an extensive set of synthetic LFR benchmark datasets.