Matrix Profile XXX: MADRID: A Hyper-Anytime and Parameter-Free Algorithm to Find Time Series Anomalies of all Lengths

Yue Lu, Thirumalai Vinjamoor Akhil Srinivas, Takaaki Nakamura, Makoto Imamura, Eamonn J. Keogh

Abstract: In recent years there has been increasing evidence that one of the simplest time series anomaly detection methods, time series discords, remains one of the most effective methods. However, time series discords have one notable issue; the anomalies discovered depend on the algorithm’s only input parameter, the subsequence length. The obvious way to bypass this issue is to find anomalies at every possible length, however this seems to be untenably slow. In this work we introduce MADRID, an algorithm to efficiently solve the all-discords problem. We show that we can reduce the absolute time to compute all-discords, and that by using a novel computation ordering strategy, MADRID is a Hyper-Anytime Algorithm. We will formally define this term later, but this refers to an anytime algorithm that converges exceptionally fast. In practice this means that for most real-world analytical tasks, the user can interact with their data in real-time. The ability to compute anomalies of all lengths produces the issue of ranking anomalies of different lengths. We further introduce novel algorithms for this task. We demonstrate the utility of MADRID in various domains and show that it allows us to Find anomalies that would otherwise escape our attention.