Studying metabolic networks is vital for many areas such as novel drugs and bio-fuels. For biologists, a key challenge is that many reactions are impractical or expensive to be found through experiments. Our task is to recover the missing reactions. By exploiting the problem structure, we model reaction recovery as a hyperlink prediction problem, where each reaction is regarded as a hyperlink connecting its participating vertices (metabolites). Different from the traditional link prediction problem where two nodes form a link, a hyperlink can involve an arbitrary number of nodes. Since the cardinality of a hyperlink is variable, existing classifiers based on a fixed number of input features become infeasible. Traditional methods, such as common neighbors and Katz index, are not applicable either, since they are restricted to pairwise similarities. In this paper, we propose a novel hyperlink prediction algorithm, called Matrix Boosting (MATBoost). MATBoost conducts inference jointly in the incidence space and adjacency space by performing an iterative completion-matching optimization. We carry out extensive experiments to show that MATBoost achieves state-of-the-art performance. For a metabolic network with 1805 metabolites and 2583 reactions, our algorithm can successfully recover nearly 200 reactions out of 400 missing reactions.
Predicting the existence of links between pairwise objects in networks is a key problem in the study of social networks. However, relationships among objects are often more complex than simple pairwise relations. By restricting attention to dyads, it is possible that information valuable for many learning tasks can be lost. The hypernetwork relaxes the assumption that only two nodes can participate in a link, permitting instead an arbitrary number of nodes to participate in so-called hyperlinks or hyperedges, which is a more natural representation for complex, multi-party relations. However, the hyperlink prediction problem has yet to be studied. In this paper, we propose HPLSF (Hyperlink Prediction using Latent Social Features), a hyperlink prediction algorithm for hypernetworks. By exploiting the homophily property of social networks, HPLSF explores social features for hyperlink prediction. To handle the problem that social features are not always observable, a latent social feature learning scheme is developed. To cope with the arbitrary cardinality hyperlink issue in hypernetworks, we design a feature-embedding scheme to map the a priori arbitrarily-sized feature set associated with each hyperlink into a uniformly-sized auxiliary space. To address the fact that observed features and latent features may be not independent, we generalize a structural SVM to learn using both observed features and latent features. In experiments, we evaluate the proposed HPLSF framework on three large-scale hypernetwork datasets. Our results on the three diverse datasets demonstrate the effectiveness of the HPLSF algorithm. Although developed in the context of social networks, HPLSF is a general methodology and applies to arbitrary hypernetworks.