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Statistical evaluation of spectral methods for anomaly detection in static networks

Published online by Cambridge University Press:  23 September 2019

Tomilayo Komolafe Open the ORCID record for Tomilayo Komolafe [Opens in a new window] ,
A. Valeria Quevedo Open the ORCID record for A. Valeria Quevedo [Opens in a new window] ,
Srijan Sengupta Open the ORCID record for Srijan Sengupta [Opens in a new window]  and
William H. Woodall
Tomilayo Komolafe*
Affiliation:
Statistics Department, Virginia Polytechnic Institute and State University, Blacksburg VA, USA (e-mails: sengupta@vt.edu; bwoodall@vt.edu)
A. Valeria Quevedo
Affiliation:
Statistics Department, Virginia Polytechnic Institute and State University, Blacksburg VA, USA (e-mails: sengupta@vt.edu; bwoodall@vt.edu) Faculty of Engineering, Universidad de Piura, Peru (e-mail: anavq@vt.edu)
Srijan Sengupta
Affiliation:
Statistics Department, Virginia Polytechnic Institute and State University, Blacksburg VA, USA (e-mails: sengupta@vt.edu; bwoodall@vt.edu)
William H. Woodall
Affiliation:
Statistics Department, Virginia Polytechnic Institute and State University, Blacksburg VA, USA (e-mails: sengupta@vt.edu; bwoodall@vt.edu)
*
*Corresponding author. Email: tomilayo@vt.edu
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Abstract

The topic of anomaly detection in networks has attracted a lot of attention in recent years, especially with the rise of connected devices and social networks. Anomaly detection spans a wide range of applications, from detecting terrorist cells in counter-terrorism efforts to identifying unexpected mutations during ribonucleic acid transcription. Fittingly, numerous algorithmic techniques for anomaly detection have been introduced. However, to date, little work has been done to evaluate these algorithms from a statistical perspective. This work is aimed at addressing this gap in the literature by carrying out statistical evaluation of a suite of popular spectral methods for anomaly detection in networks. Our investigation on the statistical properties of these algorithms reveals several important and critical shortcomings that we make methodological improvements to address. Further, we carry out a performance evaluation of these algorithms using simulated networks and extend the methods from binary to count networks.

Keywords

residual matrixspectral methodsR-MAT modelprincipal components
Type
Original Article
Information
Network Science , Volume 7 , Issue 3 , September 2019 , pp. 319 - 352
Copyright
© Cambridge University Press 2019 

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