The Graph Neural Network Model

Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs. In this paper, we propose a new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains. This GNN model, which can directly process most of the practically useful types of graphs, e.g., acyclic, cyclic, directed, and undirected, implements a function tau(G,n) isin IR^m that maps a graph G and one of its nodes n into an m-dimensional Euclidean space. A supervised learning algorithm is derived to estimate the parameters of the proposed GNN model. The computational cost of the proposed algorithm is also considered. Some experimental results are shown to validate the proposed learning algorithm, and to demonstrate its generalization capabilities.

I. Introduction

Data can be naturally represented by graph structures in several application areas, including proteomics [1], image analysis [2], scene description [3], [4], software engineering [5], [6], and natural language processing [7]. The simplest kinds of graph structures include single nodes and sequences. But in several applications, the information is organized in more complex graph structures such as trees, acyclic graphs, or cyclic graphs. Traditionally, data relationships exploitation has been the subject of many studies in the community of inductive logic programming and, recently, this research theme has been evolving in different directions [8], also because of the applications of relevant concepts in statistics and neural networks to such areas (see, for example, the recent workshops [9]–[12]).