Local spectral diffusion for robust community detection

We address a semi-supervised learning problem of identifying all latent members of a local community from very few labeled seed members in large networks. By a simple and efficient sampling method, we conduct a comparatively small subgraph encompassing most of the latent members such that the follow-up membership identification could focus on an accurate local region instead of the whole network. Then we look for a sparse vector, a relaxed indicator vector representing the subordinative probability of the corresponding nodes, that lies in a local spectral subspace defined by an order-d Krylov subspace. The subspace serves as a local proxy for the invariant subspace spanned by leading eigenvectors of the Laplacian matrices. Based on Rayleigh quotients, we relate the local membership identification task as a local RatioCut or local normalized cut optimization problem, and provide some theoretical justifications. We thoroughly explore different probability diffusion methods for the subspace definition and evaluate our method on four groups with a total of 28 representative LFR benchmark datasets, and eight publicly available real-world networks with labeled ground truth communities across multiple domains. Experimental results exhibit the effectiveness and robustness of the proposed algorithm, and the local spectral communities perform better than those from the celebrated Heat Kernel diffusion [10] and the PageRank diffusion [1].