A kernel-based nonparametric test for anomaly detection over line networks

Shaofeng Zou, Yingbin Liang, H. Vincent Poor

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

3 Scopus citations

Abstract

The nonparametric problem of detecting existence of an anomalous interval over a one-dimensional line network is studied. Nodes corresponding to an anomalous interval (if one exists) receive samples generated by a distribution q, which is different from the distribution p that generates samples for other nodes. If an anomalous interval does not exist, then all nodes receive samples generated by p. It is assumed that the distributions p and q are arbitrary, and are unknown. In order to detect whether an anomalous interval exists, a test is built based on mean embeddings of distributions into a reproducing kernel Hilbert space (RKHS) and the metric of maximum mean discrepancy (MMD). It is shown that as the network size n goes to infinity, if the minimum length of candidate anomalous intervals is larger than a threshold which has the order O(log n), the proposed test is asymptotically successful. An efficient algorithm to perform the test with substantial computational complexity reduction is proposed, and is shown to be asymptotically successful if the condition on the minimum length of candidate anomalous interval is satisfied. Numerical results are provided, which are consistent with the theoretical results.

Original languageEnglish (US)
Title of host publicationIEEE International Workshop on Machine Learning for Signal Processing, MLSP
EditorsTulay Adali, Jan Larsen, Mamadou Mboup, Eric Moreau
PublisherIEEE Computer Society
ISBN (Electronic)9781479936946
DOIs
StatePublished - Nov 14 2014
Event2014 24th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2014 - Reims, France
Duration: Sep 21 2014Sep 24 2014

Publication series

NameIEEE International Workshop on Machine Learning for Signal Processing, MLSP
ISSN (Print)2161-0363
ISSN (Electronic)2161-0371

Other

Other2014 24th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2014
CountryFrance
CityReims
Period9/21/149/24/14

All Science Journal Classification (ASJC) codes

  • Human-Computer Interaction
  • Signal Processing

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  • Cite this

    Zou, S., Liang, Y., & Poor, H. V. (2014). A kernel-based nonparametric test for anomaly detection over line networks. In T. Adali, J. Larsen, M. Mboup, & E. Moreau (Eds.), IEEE International Workshop on Machine Learning for Signal Processing, MLSP [6958913] (IEEE International Workshop on Machine Learning for Signal Processing, MLSP). IEEE Computer Society. https://doi.org/10.1109/MLSP.2014.6958913