AURORA: A Unified fRamework fOR Anomaly detection on multivariate time series

The ability to accurately and consistently discover anomalies in time series is important in many applications. Fields such as finance (fraud detection), information security (intrusion detection), healthcare, and others all benefit from anomaly detection. Intuitively, anomalies in time series are time points or sequences of time points that deviate from normal behavior characterized by periodic oscillations and long-term trends. For example, the typical activity on e-commerce websites exhibits weekly periodicity and grows steadily before holidays. Similarly, domestic usage of electricity exhibits daily and weekly oscillations combined with long-term season-dependent trends. How can we accurately detect anomalies in such domains while simultaneously learning a model for normal behavior? We propose a robust offline unsupervised framework for anomaly detection in seasonal multivariate time series, called AURORA. A key innovation in our framework is a general background behavior model that unifies periodicity and long-term trends. To this end, we leverage a Ramanujan periodic dictionary and a spline-based dictionary to capture both seasonal and trend patterns. We conduct experiments on both synthetic and real-world datasets and demonstrate the effectiveness of our method. AURORA has significant advantages over existing models for anomaly detection, including high accuracy (AUC of up to 0.98), interpretability of recovered normal behavior (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$100\%$$\end{document}100% accuracy in period detection), and the ability to detect both point and contextual anomalies. In addition, AURORA is orders of magnitude faster than baselines.