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Graph link prediction in computer networks using Poisson matrix factorisation

Graph link prediction is an important task in cyber-security: relationships between entities within a computer network, such as users interacting with computers, or system libraries and the corresponding processes that use them, can provide key insights into adversary behaviour. Poisson matrix factorisation (PMF) is a popular model for link prediction in large networks, particularly useful for its scalability. In this article, PMF is extended to include scenarios that are commonly encountered in cyber-security applications. Specifically, an extension is proposed to explicitly handle binary adjacency matrices and include known categorical covariates associated with the graph nodes. A seasonal PMF model is also presented to handle seasonal networks. To allow the methods to scale to large graphs, variational methods are discussed for performing fast inference. The results show an improved performance over the standard PMF model and other statistical network models.