Randomized spectral co-clustering for large-scale directed networks

Directed networks are generally used to represent asymmetric relationships among units. Co-clustering aims to cluster the senders and receivers of directed networks simultaneously. In particular, the well-known spectral clustering algorithm could be modified as the spectral co-clustering to co-cluster directed networks. However, large-scale networks pose computational challenge to it. In this paper, we leverage randomized sketching techniques to accelerate the spectral co-clustering algorithms in order to co-cluster large-scale directed networks more efficiently. Specifically, we derive two series of randomized spectral co-clustering algorithms, one is random-projection-based and the other is random-samplingbased. Theoretically, we analyze the resulting algorithms under two generative models-the stochastic co-block model and the degree corrected stochastic co-block model. The approximation error rates and misclustering error rates of proposed two randomized spectral co-clustering algorithms are established, which indicate better bounds than the state-ofthe-art results of co-clustering literature. Numerically, we conduct simulations to support our theoretical results and test the efficiency of the algorithms on real networks with up to tens of millions of nodes. In order to use the proposed algorithms more conveniently, a new R package called RandClust is developed and made available to the public.