  We consider the problem of link prediction in networks whose edge structure
may vary (sufficiently slowly) over time. This problem, with applications in
many important areas including social networks, has two main variants: the
first, known as positive link prediction or PLP consists in estimating the
appearance of a link in the network. The second, known as negative link
prediction or NLP consists in estimating the disappearance of a link in the
network. We propose a data-driven approach to estimate the
appearance/disappearance of edges. Our solution is based on a regularized
optimization problem for which we prove existence and uniqueness of the optimal
solution.
