Unsupervised nonparametric anomaly detection: A kernel method

Shaofeng Zou, Yingbin Liang, H. Vincent Poor, Xinghua Shi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

An anomaly detection problem is investigated, in which s out of n sequences are anomalous and need to be detected. Each sequence consists of m independent and identically distributed (i.i.d.) samples drawn either from a nominal distribution p or from an anomalous distribution q that is distinct from p. Neither p nor q is known a priori. Two scenarios respectively with s known and unknown are studied. Distribution-free tests are constructed based on the metric of the maximum mean discrepancy (MMD). It is shown that if the value of s is known, as n goes to infinity, the number m of samples in each sequence should be of order O(log n) or larger to guarantee that the constructed test is exponentially consistent. On the other hand, if the value of s is unknown, the number m of samples in each sequence should be of the order strictly greater than O(log n) to guarantee the constructed test is consistent. The computational complexity of all tests are shown to be polynomial. Numerical results are provided to confirm the theoretic characterization of the performance. Further numerical results on both synthetic data sets and real data sets demonstrate that the MMD-based tests outperform or perform as well as other approaches.

Original languageEnglish (US)
Title of host publication2014 52nd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages836-841
Number of pages6
ISBN (Print)9781479980093
DOIs
StatePublished - Jan 30 2014
Event2014 52nd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2014 - Monticello, United States
Duration: Sep 30 2014Oct 3 2014

Other

Other2014 52nd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2014
CountryUnited States
CityMonticello
Period9/30/1410/3/14

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Science Applications

Fingerprint Dive into the research topics of 'Unsupervised nonparametric anomaly detection: A kernel method'. Together they form a unique fingerprint.

  • Cite this

    Zou, S., Liang, Y., Poor, H. V., & Shi, X. (2014). Unsupervised nonparametric anomaly detection: A kernel method. In 2014 52nd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2014 (pp. 836-841). [7028541] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ALLERTON.2014.7028541