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Real-world complex networks describe connections between objects; in reality,those objects are often endowed with some kind of features. How does thepresence or absence of such features interplay with the network link structure?Although the situation here described is truly ubiquitous, there is a limitedbody of research dealing with large graphs of this kind. Many previous worksconsidered homophily as the only possible transmission mechanism translatingnode features into links. Other authors, instead, developed more sophisticatedmodels, that are able to handle complex feature interactions, but are unfit toscale to very large networks. We expand on the MGJ model, where interactionsbetween pairs of features can foster or discourage link formation. In thiswork, we will investigate how to estimate the latent feature-featureinteractions in this model. We shall propose two solutions: the first oneassumes feature independence and it is essentially based on Naive Bayes; thesecond one, which relaxes the independence assumption assumption, is based onperceptrons. In fact, we show it is possible to cast the model equation inorder to see it as the prediction rule of a perceptron. We analyze howclassical results for the perceptrons can be interpreted in this context; then,we define a fast and simple perceptron-like algorithm for this task, which canprocess $10^8$ links in minutes. We then compare these two techniques, firstwith synthetic datasets that follows our model, gaining evidence that the Naiveindependence assumptions are detrimental in practice. Secondly, we consider areal, large-scale citation network where each node (i.e., paper) can bedescribed by different types of characteristics; there, our algorithm canassess how well each set of features can explain the links, and thus findingmeaningful latent feature-feature interactions.

Estimating latent feature-feature interactions in large feature-rich graphs