Randomized Spectral Clustering in Large-Scale Stochastic Block Models

Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenge to it. In this paper, we study spectral using randomized sketching algorithms from a statistical perspective, where typically assume network data are generated stochastic block model. To do this, first use recent developed derive two algorithms, namely, random projection-based and sampling-based clustering. Then theoretical bounds resulting terms approximation error population adjacency matrix, misclustering error, estimation link probability matrix. It turns out that, under mild conditions, perform similarly original one. We also conduct numerical experiments support findings.