TY - GEN

T1 - A kernel-based nonparametric test for anomaly detection over line networks

AU - Zou, Shaofeng

AU - Liang, Yingbin

AU - Poor, H. Vincent

N1 - Publisher Copyright:
© 2014 IEEE.

PY - 2014/11/14

Y1 - 2014/11/14

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84912570457&partnerID=8YFLogxK

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U2 - 10.1109/MLSP.2014.6958913

DO - 10.1109/MLSP.2014.6958913

M3 - Conference contribution

AN - SCOPUS:84912570457

T3 - IEEE International Workshop on Machine Learning for Signal Processing, MLSP

BT - IEEE International Workshop on Machine Learning for Signal Processing, MLSP

A2 - Mboup, Mamadou

A2 - Adali, Tulay

A2 - Moreau, Eric

A2 - Larsen, Jan

PB - IEEE Computer Society

T2 - 2014 24th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2014

Y2 - 21 September 2014 through 24 September 2014

ER -