Novel semi-metrics for multivariate change point analysis and anomaly detection

PHYSICA D-NONLINEAR PHENOMENA

卷:412

Article

James, Nick¹  Menzies, Max²  Azizi, Lamiae¹  Chan, Jennifer¹ 

[1] Univ Sydney, Sch Math & Stat, Sydney, NSW, Australia

[2] Tsinghua Univ, Yau Math Sci Ctr, Beijing, Peoples R China

关键词: Semi-metrics;    Change-point detection;    Multivariate analysis;    Time series;    Anomaly detection;   

DOI  :  10.1016/j.physd.2020.132636

来源: Elsevier

【 摘 要 】

This paper proposes a new method for determining similarity and anomalies between time series, most practically effective in large collections of (likely related) time series, by measuring distances between structural breaks within such a collection. We introduce a class of semi-metric distance measures, which we term MJ distances. These semi-metrics provide an advantage over existing options such as the Hausdorff and Wasserstein metrics. We prove they have desirable properties, including better sensitivity to outliers, while experiments on simulated data demonstrate that they uncover similarity within collections of time series more effectively. Semi-metrics carry a potential disadvantage: without the triangle inequality, they may not satisfy a transitivity property of closeness.'' We analyse this failure with proof and introduce an computational method to investigate, in which we demonstrate that our semi-metrics violate transitivity infrequently and mildly. Finally, we apply our methods to cryptocurrency and measles data, introducing a judicious application of eigenvalue analysis. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free