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arXiv 1502.01783cs.LGstat.ML
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从$K$ - NN图中学习有效的异常检测器

Learning Efficient Anomaly Detectors from $K$-NN Graphs

Boston University(波士顿大学)

Jing Qian, Jonathan Root, Venkatesh Saligrama

摘要:

提出了一种高维数据的非参数异常检测算法。我们通过平均$K$ -NN距离对每个数据点进行评分,并相应地对它们进行排名。然后,我们训练有限的复杂度模型来模仿这些分数的基础上的最大利润率学习排名框架。如果预测分数在$α$百分位数内,则将测试点声明为$α$ -假警报水平的异常。所得到的异常检测器被证明是渐近最优的,在任何虚警率$α$,其决策区域收敛到$α$百分位数的最小体积水平集的未知的底层密度。此外,我们测试了我们的算法的统计性能和计算效率上的一些合成和真实数据的实验。我们的研究结果表明,我们的算法优于现有的$K$ -NN基于异常检测算法,具有显着的计算节省。

英文摘要:

We propose a non-parametric anomaly detection algorithm for high dimensional data. We score each datapoint by its average $K$-NN distance, and rank them accordingly. We then train limited complexity models to imitate these scores based on the max-margin learning-to-rank framework. A test-point is declared as an anomaly at $α$-false alarm level if the predicted score is in the $α$-percentile. The resulting anomaly detector is shown to be asymptotically optimal in that for any false alarm rate $α$, its decision region converges to the $α$-percentile minimum volume level set of the unknown underlying density. In addition, we test both the statistical performance and computational efficiency of our algorithm on a number of synthetic and real-data experiments. Our results demonstrate the superiority of our algorithm over existing $K$-NN based anomaly detection algorithms, with significant computational savings.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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