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Directed networks are broadly used to represent asymmetric relationshipsamong units. Co-clustering aims to cluster the senders and receivers ofdirected networks simultaneously. In particular, the well-known spectralclustering algorithm could be modified as the spectral co-clustering toco-cluster directed networks. However, large-scale networks pose greatcomputational challenges to it. In this paper, we leverage sketching techniquesand derive two randomized spectral co-clustering algorithms, one\emph{random-projection-based} and the other \emph{random-sampling-based}, toaccelerate the co-clustering of large-scale directed networks. We theoreticallyanalyze the resulting algorithms under two generative models -- the stochasticco-block model and the degree-corrected stochastic co-block model, andestablish their approximation error rates and misclustering error rates,indicating better bounds than the state-of-the-art results of co-clusteringliterature. Numerically, we design and conduct simulations to support ourtheoretical results and test the efficiency of the algorithms on real networkswith up to millions of nodes. A publicly available R package \textsf{RandClust}is developed for better usability and reproducibility of the proposed methods.

Randomized spectral co-clustering for large-scale directed networks