A kernel-based nonparametric test for anomaly detection over line networks
A kernel-based nonparametric test for anomaly detection over line networks
复制标题
用于线路网络异常检测的基于内核的非参数测试
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
H. Poor
中科院分区：
文献类型：
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作者：
Shaofeng Zou;Yingbin Liang;H. Poor
研究了一维线性网络上异常区间存在的非参数检测问题。对应于异常间隔(如果存在)的节点接收由分布q生成的样本，该分布不同于为其他节点生成样本的分布p。如果不存在异常区间，则所有节点都接收由p生成的样本。假设分布p和q是任意的，并且是未知的。为了检测是否存在异常区间，基于分布在再生核希尔伯特空间(RKHS)中的平均嵌入和最大平均偏差(MMD)度量建立了检验。结果表明，当网络规模n趋于无穷大时，如果候选异常区间的最小长度大于O(Logn)阶的阈值，则所提出的检验是渐近成功的。提出了一种有效的测试算法，大大降低了计算复杂度，并证明了在满足候选异常区间最小长度的条件下，该算法是渐近成功的。给出了数值结果，与理论结果相吻合。
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.