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Community detection is an important information mining task to uncovermodular structures in large networks. For increasingly common large networkdata sets, global community detection is prohibitively expensive, and attentionhas shifted to methods that mine local communities, i.e. identifying all latentmembers of a particular community from a few labeled seed members. To addresssuch semi-supervised mining task, we systematically develop a local spectralsubspace-based community detection method, called LOSP. We define a family oflocal spectral subspaces based on Krylov subspaces, and seek a sparse indicatorfor the target community via an $\ell_1$ norm minimization over the Krylovsubspace. Variants of LOSP depend on type of random walks with differentdiffusion speeds, type of random walks, dimension of the local spectralsubspace and step of diffusions. The effectiveness of the proposed LOSPapproach is theoretically analyzed based on Rayleigh quotients, and it isexperimentally verified on a wide variety of real-world networks across social,production and biological domains, as well as on an extensive set of syntheticLFR benchmark datasets.

Krylov Subspace Approximation for Local Community Detection in Large Networks