Detecting anomalies in data is a vital task, with numerous high-impact applications in areas such as security, finance, health care, and law enforcement. While numerous techniques have been developed in past years for spotting outliers and anomalies in unstructured collections of multi-dimensional points, with graph data becoming ubiquitous, techniques for structured graph data have been of focus recently. As objects in graphs have long-range correlations, a suite of novel technology has been developed for anomaly detection in graph data. This survey aims to provide a general, comprehensive, and structured overview of the state-of-the-art methods for anomaly detection in data represented as graphs. As a key contribution, we give a general framework for the algorithms categorized under various settings: unsupervised versus (semi-)supervised approaches, for static versus dynamic graphs, for attributed versus plain graphs. We highlight the effectiveness, scalability, generality, and robustness aspects of the methods. What is more, we stress the importance of anomaly attribution and highlight the major techniques that facilitate digging out the root cause, or the `why', of the detected anomalies for further analysis and sense-making. Finally, we present several real-world applications of graph-based anomaly detection in diverse domains, including financial, auction, computer traffic, and social networks. We conclude our survey with a discussion on open theoretical and practical challenges in the field.

http://www3.cs.stonybrook.edu/~leman/pubs/14-dami-graphanomalysurvey.pdf

Graph based anomaly detection and description: a survey

Detecting anomalies in data is a vital task, with numerous high-impact applications in areas such as security, finance, health care, and law enforcement. While numerous techniques have been developed in past years for spotting outliers and anomalies in unstructured collections of multi-dimensional points, with graph data becoming ubiquitous, techniques for structured {\em graph} data have been of focus recently. As objects in graphs have long-range correlations, a suite of novel technology has been developed for anomaly detection in graph data. 
This survey aims to provide a general, comprehensive, and structured overview of the state-of-the-art methods for anomaly detection in data represented as graphs. As a key contribution, we provide a comprehensive exploration of both data mining and machine learning algorithms for these {\em detection} tasks. we give a general framework for the algorithms categorized under various settings: unsupervised vs. (semi-)supervised approaches, for static vs. dynamic graphs, for attributed vs. plain graphs. We highlight the effectiveness, scalability, generality, and robustness aspects of the methods. What is more, we stress the importance of anomaly {\em attribution} and highlight the major techniques that facilitate digging out the root cause, or the `why', of the detected anomalies for further analysis and sense-making. Finally, we present several real-world applications of graph-based anomaly detection in diverse domains, including financial, auction, computer traffic, and social networks. We conclude our survey with a discussion on open theoretical and practical challenges in the field.

Graph-based Anomaly Detection and Description: A Survey

A special class of graphs is introduced in this paper. The graphs belonging to this class are characterised by the existence of unique node labels. A number of matching algorithms for graphs with unique node labels are developed. It is shown that problems such as graph isomorphism, subgraph isomorphism, maximum common subgraph (MCS) and graph edit distance (GED) have a computational complexity that is only quadratic in the number of nodes. Moreover, computing the median of a set of graphs is only linear in the cardinality of the set. In a series of experiments, it is demonstrated that the proposed algorithms run very fast in practice. The considered class makes the matching of large graphs, consisting of thousands of nodes, computationally tractable. We also discuss an application of the considered class of graphs and related matching algorithms to the classification and detection of abnormal events in computer networks.

Matching graphs with unique node labels

Anomalies are occurrences in a dataset that are in some way unusual and do not fit the general patterns. The concept of the anomaly is generally ill-defined and perceived as vague and domain-dependent. Moreover, no comprehensive and concrete overviews of the different types of anomalies have hitherto been published. By means of an extensive literature review this study therefore offers the first theoretically principled and domain-independent typology of data anomalies, and presents a full overview of anomaly types and subtypes. To concretely define the concept of the anomaly and its different manifestations the typology employs four dimensions: data type, cardinality of relationship, data structure and data distribution. These fundamental and data-centric dimensions naturally yield 3 broad groups, 9 basic types and 61 subtypes of anomalies. The typology facilitates the evaluation of the functional capabilities of anomaly detection algorithms, contributes to explainable data science, and provides insights into relevant topics such as local versus global anomalies.

pdf/on-the-nature-and-types-of-anomalies-a-review-1umj938wtu.pdf

On the Nature and Types of Anomalies: A Review.

The rapid development of modern communication technologies—in particular, (mobile) phone communications—has largely facilitated human social interactions and information exchange. However, the emergence of telemarketing frauds can significantly dissipate individual fortune and social wealth, resulting in a potential slow down or damage to economics. In this work, we propose to spot telemarketing frauds, with an emphasis on unveiling the “ precise fraud ” phenomenon and the strategies that are used by fraudsters to precisely select targets. To study this problem, we employ a one-month complete dataset of telecommunication metadata in Shanghai with 54 million users and 698 million call logs. Through our study, we find that user's information might have been seriously leaked, and fraudsters have a preference over the target user's age and activity in mobile network. We further propose a novel semi-supervised learning framework to distinguish fraudsters from non-fraudsters. Experimental results on a real-world data show that our approach outperforms several state-of-the-art algorithms in accuracy of detecting fraudsters (e.g., $+0.278$ + 0 . 278 in terms of F1 on average). We believe that our study can potentially inform policymaking for government and mobile service providers.

Mining Fraudsters and Fraudulent Strategies in Large-Scale Mobile Social Networks

In the management of large enterprise communication networks, it becomes difficult to detect and identify causes of abnormal change in traffic distributions when the underlying logical topology is ...

Detection of abnormal change in a time series of graphs

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Detection of abnormal change in a time series of graphs