Classification in biological networks with hypergraphlet kernels

Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties between these objects (binds-to, interacts-with, regulates). This approach has been highly successful owing to the theory, methodology and software that support analysis and learning on graphs. Graphs, however, suffer from information loss when modeling physical systems due to their inability to accurately represent multi-object relationships. Hypergraphs, a generalization of graphs, provide a framework to mitigate information loss and unify disparate graph-based methodologies. We present a hypergraph-based approach for modeling biological systems and formulate vertex classification, edge classification and link prediction problems on (hyper)graphs as instances of vertex classification on (extended, dual) hypergraphs. We then introduce a novel kernel method on vertex- and edge-labeled (colored) hypergraphs for analysis and learning. The method is based on exact and inexact (via hypergraph edit distances) enumeration of hypergraphlets; i.e., small hypergraphs rooted at a vertex of interest. We empirically evaluate this method on fifteen biological networks and show its potential use in a positive-unlabeled setting to estimate the interactome sizes in various species.