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 IRm 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.

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The Graph Neural Network Model

Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented in the Euclidean space. However, there is an increasing number of applications, where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. The complexity of graph data has imposed significant challenges on the existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this article, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields. We propose a new taxonomy to divide the state-of-the-art GNNs into four categories, namely, recurrent GNNs, convolutional GNNs, graph autoencoders, and spatial–temporal GNNs. We further discuss the applications of GNNs across various domains and summarize the open-source codes, benchmark data sets, and model evaluation of GNNs. Finally, we propose potential research directions in this rapidly growing field.

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A Comprehensive Survey on Graph Neural Networks

Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics systems, learning molecular fingerprints, predicting protein interface, and classifying diseases demand a model to learn from graph inputs. In other domains such as learning from non-structural data like texts and images, reasoning on extracted structures (like the dependency trees of sentences and the scene graphs of images) is an important research topic which also needs graph reasoning models. Graph neural networks (GNNs) are neural models that capture the dependence of graphs via message passing between the nodes of graphs. In recent years, variants of GNNs such as graph convolutional network (GCN), graph attention network (GAT), graph recurrent network (GRN) have demonstrated ground-breaking performances on many deep learning tasks. In this survey, we propose a general design pipeline for GNN models and discuss the variants of each component, systematically categorize the applications, and propose four open problems for future research.

Graph Neural Networks: A Review of Methods and Applications

Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous node and edge attributes. Analogous to image-based convolutional networks that operate on locally connected regions of the input, we present a general approach to extracting locally connected regions from graphs. Using established benchmark data sets, we demonstrate that the learned feature representations are competitive with state of the art graph kernels and that their computation is highly efficient.

Learning Convolutional Neural Networks for Graphs

In this article, we propose a family of efficient kernels for large graphs with discrete node labels. Key to our method is a rapid feature extraction scheme based on the Weisfeiler-Lehman test of isomorphism on graphs. It maps the original graph to a sequence of graphs, whose node attributes capture topological and label information. A family of kernels can be defined based on this Weisfeiler-Lehman sequence of graphs, including a highly efficient kernel comparing subtree-like patterns. Its runtime scales only linearly in the number of edges of the graphs and the length of the Weisfeiler-Lehman graph sequence. In our experimental evaluation, our kernels outperform state-of-the-art graph kernels on several graph classification benchmark data sets in terms of accuracy and runtime. Our kernels open the door to large-scale applications of graph kernels in various disciplines such as computational biology and social network analysis.

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Weisfeiler-Lehman Graph Kernels

A review of the literature yielded data on over 200 aromatic and heteroaromatic nitro compounds tested for mutagenicity in the Ames test using S. typhimurium TA98. From the data, a quantitative structure-activity relationship (QSAR) has been derived for 188 congeners. The main determinants of mutagenicity are the hydrophobicity (modeled by octanol/water partition coefficients) and the energies of the lowest unoccupied molecular orbitals calculated using the AM1 method. It is also shown that chemicals possessing three or more fused rings possess much greater mutagenic potency than compounds with one or two fused rings. Since the QSAR is based on a very wide range in structural variation, aromatic rings from benzene to coronene are included as well as many different types of heterocycles, it is a significant step toward a predictive toxicology of value in the design of less mutagenic bioactive compounds.

Structure-activity relationship of mutagenic aromatic and heteroaromatic nitro compounds. Correlation with molecular orbital energies and hydrophobicity.

A set of 36 congeneric 4-aminodiphenyl sulfones with measured inhibition potencies of dihydropteroate synthase were studied by using both linear free energy and molecular modeling methods. The goals of the investigation were to identify the "active" conformation for these compounds as inhibitors and, correspondingly, to contruct a quantitative structure-activity relationship (QSAR). These molecules are quite flexible and possess multiple conformational energy minima. Application of molecular shape analysis (MSA), using all intramolecular energy minima as part of the analysis, was not successful in generating a QSAR. However, the calculated intramolecular conformational entropy of these compounds was found to correlate with inhibition potency leading to a highly significant QSAR. Inhibition potency increases as entropy decreases. A decrease in entropy enhances the population of specific, symmetry-related minimum-energy conformations. In this indirect way, it was possible to postulate an "active" conformation. This investigation illustrates that specific knowledge of the "active" shape of a molecule may not provide the information needed to quantitatively explain the observed structure-activity relationship.

A quantitative structure-activity relationship analysis of some 4-aminodiphenyl sulfone antibacterial agents using linear free energy and molecular modeling methods

Lopez de Compadre Rl

Papers

Structure-activity relationship of mutagenic aromatic and heteroaromatic nitro compounds. Correlation with molecular orbital energies and hydrophobicity.

A quantitative structure-activity relationship analysis of some 4-aminodiphenyl sulfone antibacterial agents using linear free energy and molecular modeling methods