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Link Prediction with Cardinality Constraint

Inferring the links among entities in networks is an important research problem for various disciplines. Depending on the specific application settings, the links to be inferred are usually subject to different cardinality constraints, like one-to-one, one-to-many and many-to-many. However, most existing research works on link prediction problems fail to consider such a kind of constraint. In this paper, we propose to study the link prediction problem with general cardinality constraints, which is formally defined as the CLP (Cardinality Constrained Link Prediction) problem. By minimizing the projection loss of links from feature vectors to labels, the CLP problem is formulated as an optimization problem involving multiple variables, where the cardinality constraints are modeled as mathematical constraints on node degrees. The objective function is shown to be not jointly convex and the optimal solution subject to the cardinality constraints can be very time-consuming to achieve. To solve the optimization problem, an iterative variable updating based link prediction framework ITERCLIPS (Iterative Constrained Link Prediction & Selection) is introduced in this paper, which involves the steps on link updating and selection alternatively. To overcome the high time cost problem, a greedy link selection step is introduced in this paper, which picks links greedily while preserving the link cardinality constraints simultaneously. Meanwhile, to ensure the effectiveness of ITERCLIPS on large-scale networks, a distributed implementation of ITERCLIPS is further presented as a scalable solution to the CLP problem. Extensive experiments have been done on three real-world network datasets with different types of cardinality constraints, and the experimental results achieved by ITERCLIPS on all these datasets can demonstrate the effectiveness and advantages of ITERCLIPS in solving the CLP problem.