Nonparametric detection of an anomalous disk over a two-dimensional lattice network
Shaofeng Zou, Yingbin Liang, H. Vincent Poor
Abstract
Nonparametric detection of existence of an anomalous disk over a lattice network is investigated. If an anomalous disk exists, then all nodes belonging to the disk observe samples generated by a distribution q, whereas all other nodes observe samples generated by a distribution p that is distinct from q. If there does not exist an anomalous disk, then all nodes receive samples generated by p. The distributions p and q are arbitrary and unknown. The goal is to design statistically consistent test as the network size becomes asymptotically large. A kernel-based test is proposed based on maximum mean discrepancy (MMD) which measures the distance between mean embeddings of distributions into a reproducing kernel Hilbert space (RKHS). A sufficient condition on the minimum size of candidate anomalous disks is characterized in order to guarantee the consistency of the proposed test. A necessary condition that any universally consistent test must satisfy is further derived. Comparison of sufficient and necessary conditions yields that the proposed test is order-level optimal.
BibTeX
@inproceedings{icassp2016_nonparametricdet,
title = {Nonparametric detection of an anomalous disk over a two-dimensional lattice network},
author = {Shaofeng Zou and Yingbin Liang and H. Vincent Poor},
booktitle = {ICASSP 2016},
year = {2016}
}