Abstract

--- - Detecting anomalies in time series in real time can be challenging, in particular when anomalies can manifest themselves at different time scales and need to be detected with minimal latency. The need for lightweight real-time algorithms has risen in the context of Cloud computing, where thousands of devices are monitored and deviations from normal behaviour must be detected to prevent incidents. However, this need has yet to be addressed in a way that actually scales to the size of today's network infrastructures. - Typically, time series generated by human activity often exhibit daily and weekly patterns creating long-term dependencies that are difficult to process. In such cases, the euclidean distance between subsequences of the time series, or euclidean anomaly score, can be a very effective tool to achieve good detection within constrained latency; however, this computation has a quadratic complexity and a computational footprint too high for any realistic application. - In this paper, we propose SCHEDA (Sampled Causal Heuristics for Euclidean Distance Approximation), a collection of three heuristics designed to approximate the euclidean anomaly score with a low computational footprint in time series with long-term dependencies. Our design goals are a low computational cost, the possibility of real-time operation and the absence of tuning parameters. We benchmark SCHEDA against ARIMA and the euclidean distance and show that in typical monitoring scenarios, it outperforms both at only a fraction of the computational cost. (C) 2019 Elsevier B.V. All rights reserved.