# Classification in biological networks with hypergraphlet kernels

## TL;DR

This paper introduces a hypergraphlet kernel method for modeling biological systems, improving upon traditional graph models by capturing complex multiobject relationships for tasks like classification and link prediction.

## Contribution

It presents a novel hypergraphlet kernel approach for analyzing hypergraphs, extending graph-based methods to better model biological networks with multiobject interactions.

## Key findings

- Effective in estimating missing links in protein-protein interaction networks
- Demonstrates potential in positive-unlabeled learning scenarios
- Extends graph kernels to hypergraph structures

## Abstract

Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among 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, often suffer from information loss when modeling physical systems due to their inability to accurately represent multiobject relationships. Hypergraphs, a generalization of graphs, provide a framework to mitigate information loss and unify disparate graph-based methodologies. In this paper, we present a hypergraph-based approach for modeling physical systems and formulate vertex classification, edge classification and link prediction problems on (hyper)graphs as instances of vertex classification on (extended, dual) hypergraphs in a semi-supervised setting. We 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 small simple hypergraphs, referred to as hypergraphlets, rooted at a vertex of interest. We extensively evaluate this method and show its potential use in a positive-unlabeled setting to estimate the number of missing and false positive links in protein-protein interaction networks.