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Based on the definition of local spectral subspace, we propose a novelapproach called LOSP for local overlapping community detection. Instead ofusing the invariant subspace spanned by the dominant eigenvectors of the entirenetwork, we run the power method for a few steps to approximate the leadingeigenvectors that depict the embedding of the local neighborhood structurearound seeds of interest. We then seek a sparse approximate indicator vector inthe local spectral subspace spanned by these vectors such that the seeds are inits support.  We evaluate LOSP on five large real world networks across various domainswith labeled ground-truth communities and compare the results with thestate-of-the-art community detection approaches. LOSP identifies the members ofa target community with high accuracy from very few seed members, andoutperforms the local Heat Kernel or PageRank diffusions as well as the globalbaselines.  Two candidate definitions of the local spectral subspace are analyzed, anddifferent community scoring functions for determining the community boundary,including two new metrics, are thoroughly evaluated. The structural propertiesof different seed sets and the impact of the seed set size are discussed. Weobserve low degree seeds behave better, and LOSP is robust even when startedfrom a single random seed.  Using LOSP as a subroutine and starting from each ego connected component, wetry the harder yet significant task of identifying all communities a singlevertex is in. Experiments show that the proposed method achieves high F1measures on the detected multiple local overlapping communities containing theseed vertex.

Detecting Overlapping Communities from Local Spectral Subspaces