TOWARDS GRAPH-LEVEL ANOMALY DETECTION VIA DEEP EVOLUTIONARY MAPPING

Abstract

Graph-level anomaly detection aims at capturing anomalous individual graphs in a graph set. Due to its significance in various real-world application fields, such as identifying rare molecules in chemistry and detecting potential frauds in online social networks, graph-level anomaly detection has received great attention. In distinction from node-and edge-level anomaly detection that is devoted to identifying anomalies on a single graph, graph-level anomaly detection faces more significant challenges because both the intraand inter-graph structural and attribute patterns need to be taken into account to distinguish anomalies that exhibit deviating structures, rare attributes or the both. Although deep graph representation learning shows effectiveness in fusing high-level representations and capturing characters of individual graphs, most of the existing works are defective in graph-level anomaly detection because of their limited capability in exploring information across graphs, the imbalanced data distribution of anomalies, and low interpretability of the black-box graph neural networks (GNNs). To overcome these limitations, we propose a novel deep evolutionary graph mapping framework named GmapAD, which can adaptively map each graph into a new feature space based on its similarity to a set of representative nodes chosen from the graph set. By automatically adjusting the candidate nodes using a specially designed evolutionary algorithm, anomalies and normal graphs are mapped to separate areas in the new feature space where a clear boundary between them can be learned. The selected candidate nodes can therefore be regarded as a benchmark for explaining anomalies because anomalies are more dissimilar/similar to the benchmark than normal graphs. Through our extensive experiments on nine real-world datasets, we demonstrate that exploring both intraand inter-graph structural and attribute information are critical to spot anomalous graphs, and our framework outperforms the state of the art on all datasets used in the experiments 1 .

1. INTRODUCTION

Graph-level anomalies are abnormal or rare individual graphs in a graph set. These anomalies can be observed in various application fields, such as rare molecules and abnormal proteins in biochemistry, brain disorders in brain networks/graphs, and frauds in online social networks (Noble & Cook, 2003; Akoglu et al., 2015) . Detecting this category of anomalies has shown great benefits in facilitating downstream anomaly handling process, alleviating anomalies' detrimental impact on society, and boosting real-world applications (e.g., health monitoring and drug discovery). However, graph-level anomaly detection differs significantly from node-and edge-level anomaly detection that investigates an individual graph. Graph-level anomaly detection targets anomalous individuals among various graphs. Not only the unique spatial structure and nodes/edges' attributes associated with each graph, but also the cross-graph structural and attribute patterns should be critically analyzed to identify these potential anomalies in the graph set (Ma et al., 2021) . Recent studies in deep graph representation have put great effort into encoding both the complex graph structural information and attribute information into vectors and then conducting graph analysis within the representation space (Wu et al., 2020) . Although plenty of graph neural networks (GNNs) have been developed to learn expressive node representations via message passing



The code is available at https://github.com/GmapAD/GmapAD 1

