Elastic Depths for Detecting Shape Anomalies in Functional Data
Elastic Depths for Detecting Shape Anomalies in Functional Data
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DOI：
10.1080/00401706.2020.1811156
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发表时间：
2019-07
期刊：
影响因子：
2.5
通讯作者：
Trevor Harris;J. Tucker;Bo Li;L. Shand
中科院分区：
文献类型：
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作者：
Trevor Harris;J. Tucker;Bo Li;L. Shand
摘要本文提出了一种新的深度测度族-弹性深度测度，它可以大大提高函数数据中形状异常的检测能力。形状异常是具有与其余数据相当不同的几何形式或特征的函数。识别它们通常比识别震级异常更困难，因为形状异常通常无法用可视化方法从大量数据中区分出来。建议的弹性深度使用最近开发的弹性距离直接测量的振幅和相位空间中的功能的中心。在这些空间中测量形状异常度提供了形状的严格量化，这使得弹性深度在检测形状异常方面比其他方法具有强大的理论和实践优势。一个简单的箱形图和阈值的方法来识别形状异常使用的弹性深度。我们评估的弹性深度的检测技巧模拟形状异常的情况下，并将它们与流行的形状异常检测器。最后，我们使用飓风轨迹来演示弹性深度方法在流形值函数数据。
Abstract We propose a new family of depth measures called the elastic depths that can be used to greatly improve shape anomaly detection in functional data. Shape anomalies are functions that have considerably different geometric forms or features from the rest of the data. Identifying them is generally more difficult than identifying magnitude anomalies because shape anomalies are often not distinguishable from the bulk of the data with visualization methods. The proposed elastic depths use the recently developed elastic distances to directly measure the centrality of functions in the amplitude and phase spaces. Measuring shape outlyingness in these spaces provides a rigorous quantification of shape, which gives the elastic depths a strong theoretical and practical advantage over other methods in detecting shape anomalies. A simple boxplot and thresholding method is introduced to identify shape anomalies using the elastic depths. We assess the elastic depth’s detection skill on simulated shape outlier scenarios and compare them against popular shape anomaly detectors. Finally, we use hurricane trajectories to demonstrate the elastic depth methodology on manifold valued functional data.