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Analytical models and methods for anomaly detection in dynamic, attributed graphs

Published in:
Chapter 2, Computational Network Analysis with R: Applications in Biology, Medicine, and Chemistry, 2017, pp. 35-61.

Summary

This chapter is devoted to anomaly detection in dynamic, attributed graphs. There has been a great deal of research on anomaly detection in graphs over the last decade, with a variety of methods proposed. This chapter discusses recent methods for anomaly detection in graphs,with a specific focus on detection within backgrounds based on random graph models. This sort of analysis can be applied for a variety of background models, which can incorporate topological dynamics and attributes of vertices and edges. The authors have developed a framework for anomalous subgraph detection in random background models, based on linear algebraic features of a graph. This includes an implementation in R that exploits structure in the random graph model for computationally tractable analysis of residuals. This chapter outlines this framework within the context of analyzing dynamic, attributed graphs. The remainder of this chapter is organized as follows. Section 2.2 defines the notation used within the chapter. Section 2.3 briefly describes a variety of perspectives and techniques for anomaly detection in graph-based data. Section 2.4 provides an overview of models for graph behavior that can be used as backgrounds for anomaly detection. Section 2.5 describes our framework for anomalous subgraph detection via spectral analysis of residuals, after the data are integrated over time. Section 2.6 discusses how the method described in Section 2.5 can be efficiently implemented in R using open source packages. Section 2.7 demonstrates the power of this technique in controlled simulation, considering the effects of both dynamics and attributes on detection performance. Section 2.8 gives a data analysis example within this context, using an evolving citation graph based on a commercially available document database of public scientific literature. Section 2.9 summarizes the chapter and discusses ongoing research in this area.
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Summary

This chapter is devoted to anomaly detection in dynamic, attributed graphs. There has been a great deal of research on anomaly detection in graphs over the last decade, with a variety of methods proposed. This chapter discusses recent methods for anomaly detection in graphs,with a specific focus on detection within...

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Very large graphs for information extraction (VLG) - detection and inference in the presence of uncertainty

Summary

In numerous application domains relevant to the Department of Defense and the Intelligence Community, data of interest take the form of entities and the relationships between them, and these data are commonly represented as graphs. Under the Very Large Graphs for Information Extraction effort--a one year proof-of-concept study--MIT LL developed novel techniques for anomalous subgraph detection, building on tools in the signal processing research literature. This report documents the technical results of this effort. Two datasets--a snapshot of Thompson Reuters' Web of Science database and a stream of web proxy logs--were parsed, and graphs were constructed from the raw data. From the phenomena in these datasets, several algorithms were developed to model the dynamic graph behavior, including a preferential attachment mechanism with memory, a streaming filter to model a graph as a weighted average of its past connections, and a generalized linear model for graphs where connection probabilities are determined by additional side information or metadata. A set of metrics was also constructed to facilitate comparison of techniques. The study culminated in a demonstration of the algorithms on the datasets of interest, in addition to simulated data. Performance in terms of detection, estimation, and computational burden was measured according to the metrics. Among the highlights of this demonstration were the detection of emerging coauthor clusters in the Web of Science data, detection of botnet activity in the web proxy data after 15 minutes (which took 10 days to detect using state-of-the-practice techniques), and demonstration of the core algorithm on a simulated 1-billion-vertex graph using a commodity computing cluster.
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Summary

In numerous application domains relevant to the Department of Defense and the Intelligence Community, data of interest take the form of entities and the relationships between them, and these data are commonly represented as graphs. Under the Very Large Graphs for Information Extraction effort--a one year proof-of-concept study--MIT LL developed...

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Spectral subgraph detection with corrupt observations

Published in:
Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, ICASSP, 4-9 May 2014.

Summary

Recent work on signal detection in graph-based data focuses on classical detection when the signal and noise are both in the form of discrete entities and their relationships. In practice, the relationships of interest may not be directly observable, or may be observed through a noisy mechanism. The effects of imperfect observations add another layer of difficulty to the detection problem, beyond the effects of typical random fluctuations in the background graph. This paper analyzes the impact on detection performance of several error and corruption mechanisms for graph data. In relatively simple scenarios, the change in signal and noise power is analyzed, and this is demonstrated empirically in more complicated models. It is shown that, with enough side information, it is possible to fully recover performance equivalent to working with uncorrupted data using a Bayesian approach, and a simpler cost-optimization approach is shown to provide a substantial benefit as well.
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Summary

Recent work on signal detection in graph-based data focuses on classical detection when the signal and noise are both in the form of discrete entities and their relationships. In practice, the relationships of interest may not be directly observable, or may be observed through a noisy mechanism. The effects of...

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Very large graphs for information extraction (VLG) - summary of first-year proof-of-concept study

Summary

In numerous application domains relevant to the Department of Defense and the Intelligence Community, data of interest take the form of entities and the relationships between them, and these data are commonly represented as graphs. Under the Very Large Graphs for Information Extraction effort--a one-year proof-of-concept study--MIT LL developed novel techniques for anomalous subgraph detection, building on tools in the signal processing research literature. This report documents the technical results of this effort. Two datasets--a snapshot of Thompson Reuters? Web of Science database and a stream of web proxy logs--were parsed, and graphs were constructed from the raw data. From the phenomena in these datasets, several algorithms were developed to model the dynamic graph behavior, including a preferential attachment mechanism with memory, a streaming filter to model a graph as a weighted average of its past connections, and a generalized linear model for graphs where connection probabilities are determined by additional side information or metadata. A set of metrics was also constructed to facilitate comparison of techniques. The study culminated in a demonstration of the algorithms on the datasets of interest, in addition to simulated data. Performance in terms of detection, estimation, and computational burden was measured according to the metrics. Among the highlights of this demonstration were the detection of emerging coauthor clusters in the Web of Science data, detection of botnet activity in the web proxy data after 15 minutes (which took 10 days to detect using state-of-the-practice techniques), and demonstration of the core algorithm on a simulated 1-billion-vertex graph using a commodity computing cluster.
READ LESS

Summary

In numerous application domains relevant to the Department of Defense and the Intelligence Community, data of interest take the form of entities and the relationships between them, and these data are commonly represented as graphs. Under the Very Large Graphs for Information Extraction effort--a one-year proof-of-concept study--MIT LL developed novel...

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Efficient anomaly detection in dynamic, attributed graphs: emerging phenomena and big data

Published in:
ISI 2013: IEEE Int. Conf. on Intelligence and Security Informatics, 4-7 June 2013.

Summary

When working with large-scale network data, the interconnected entities often have additional descriptive information. This additional metadata may provide insight that can be exploited for detection of anomalous events. In this paper, we use a generalized linear model for random attributed graphs to model connection probabilities using vertex metadata. For a class of such models, we show that an approximation to the exact model yields an exploitable structure in the edge probabilities, allowing for efficient scaling of a spectral framework for anomaly detection through analysis of graph residuals, and a fast and simple procedure for estimating the model parameters. In simulation, we demonstrate that taking into account both attributes and dynamics in this analysis has a much more significant impact on the detection of an emerging anomaly than accounting for either dynamics or attributes alone. We also present an analysis of a large, dynamic citation graph, demonstrating that taking additional document metadata into account emphasizes parts of the graph that would not be considered significant otherwise.
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Summary

When working with large-scale network data, the interconnected entities often have additional descriptive information. This additional metadata may provide insight that can be exploited for detection of anomalous events. In this paper, we use a generalized linear model for random attributed graphs to model connection probabilities using vertex metadata. For...

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A scalable signal processing architecture for massive graph analysis

Published in:
ICASSP 2012, Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, 25-30 March 2012, pp. 5329-32.

Summary

In many applications, it is convenient to represent data as a graph, and often these datasets will be quite large. This paper presents an architecture for analyzing massive graphs, with a focus on signal processing applications such as modeling, filtering, and signal detection. We describe the architecture, which covers the entire processing chain, from data storage to graph construction to graph analysis and subgraph detection. The data are stored in a new format that allows easy extraction of graphs representing any relationship existing in the data. The principal analysis algorithm is the partial eigendecomposition of the modularity matrix, whose running time is discussed. A large document dataset is analyzed, and we present subgraphs that stand out in the principal eigenspace of the time varying graphs, including behavior we regard as clutter as well as small, tightly-connected clusters that emerge over time.
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Summary

In many applications, it is convenient to represent data as a graph, and often these datasets will be quite large. This paper presents an architecture for analyzing massive graphs, with a focus on signal processing applications such as modeling, filtering, and signal detection. We describe the architecture, which covers the...

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Moments of parameter estimates for Chung-Lu random graph models

Published in:
ICASSP 2012, Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, 25-30 March 2012, pp. 3961-4.

Summary

As abstract representations of relational data, graphs and networks find wide use in a variety of fields, particularly when working in non- Euclidean spaces. Yet for graphs to be truly useful in in the context of signal processing, one ultimately must have access to flexible and tractable statistical models. One model currently in use is the Chung- Lu random graph model, in which edge probabilities are expressed in terms of a given expected degree sequence. An advantage of this model is that its parameters can be obtained via a simple, standard estimator. Although this estimator is used frequently, its statistical properties have not been fully studied. In this paper, we develop a central limit theory for a simplified version of the Chung-Lu parameter estimator. We then derive approximations for moments of the general estimator using the delta method, and confirm the effectiveness of these approximations through empirical examples.
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Summary

As abstract representations of relational data, graphs and networks find wide use in a variety of fields, particularly when working in non- Euclidean spaces. Yet for graphs to be truly useful in in the context of signal processing, one ultimately must have access to flexible and tractable statistical models. One...

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