  The problem of predicting links in large networks is an important task in a
variety of practical applications, including social sciences, biology and
computer security. In this paper, statistical techniques for link prediction
based on the popular random dot product graph model are carefully presented,
analysed and extended to dynamic settings. Motivated by a practical application
in cyber-security, this paper demonstrates that random dot product graphs not
only represent a powerful tool for inferring differences between multiple
networks, but are also efficient for prediction purposes and for understanding
the temporal evolution of the network. The probabilities of links are obtained
by fusing information at two stages: spectral methods provide estimates of
latent positions for each node, and time series models are used to capture
temporal dynamics. In this way, traditional link prediction methods, usually
based on decompositions of the entire network adjacency matrix, are extended
using temporal information. The methods presented in this article are applied
to a number of simulated and real-world graphs, showing promising results.
