Querying Complex Networks in Vector Space
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Learning vector embeddings of complex networks is a powerful approach used to predict missing or unobserved edges in network data. However, an open challenge in this area is developing techniques that can reason about subgraphs in network data, which can involve the logical conjunction of several edge relationships. Here we introduce a framework to make predictions about conjunctive logical queries---i.e., subgraph relationships---on heterogeneous network data. In our approach, we embed network nodes in a low-dimensional space and represent logical operators as learned geometric operations (e.g., translation, rotation) in this embedding space. We prove that a small set of geometric operations are sufficient to represent conjunctive logical queries on a network, and we introduce a series of increasingly strong implementations of these operators. We demonstrate the utility of this framework in two application studies on networks with millions of edges: predicting unobserved subgraphs in a network of drug-gene-disease interactions and in a network of social interactions derived from a popular web forum. These experiments demonstrate how our framework can efficiently make logical predictions such as "what drugs are likely to target proteins involved with both diseases X and Y?" Together our results highlight how imposing logical structure can make network embeddings more useful for large-scale knowledge discovery.
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