Unsupervised inference of statistically significant synchronization and opposition links from bipartite systems

Abstract

Many of the real-world data sets can be portrayed as bipartite networks. Such data sets are particularly abundant where human behavior is being recorded. Because typically direct observations of the relationships between different agents are lacking, they need to be inferred by converting bipartite networks to their mono-partite counterparts. While most bipartite networks contain only one type of a link, e.g., an agent attended an event, data sets exist where the links can represent different actions, say when voting, an agent supported, opposed, or abstained a proposition. This paper proposes a new unsupervised statistical method based on hypergeometric-binomial mixture distribution to identify the most significant synchronization and opposition ties between agents when they are recorded to take different actions. The method takes into account the heterogeneity of individual nodes in terms of how active they are and in terms of their preferred actions. The resulting binary or signed graphs can then be used to investigate the structure of co-behaviors between agents. We demonstrate the link validation using empirical investor trading and parliament member voting data. We find structurally balanced signed networks.