Anomaly Detection Using Causal Sliding Windows

Abstract

Anomaly detection using sliding windows is not new but using causal sliding windows has not been explored in the past. The need for causality arises from real-time processing where the used sliding windows should not include future data samples that have not been visited, i.e., those data sample vectors come in after the currently being processed data sample vector. This chapter presents an approach developed by Chang et al. (2015) to anomaly detection using causal sliding windows, which has the capability of being implemented in real time. In doing so, two types of causal windows are defined, causal sliding matrix windows including square matrix windows and rectangular matrix windows and causal sliding array windows, each of which derives a causal sample covariance/correlation matrix for causal anomaly detection. As for the causal sliding array windows, recursive update equations are also derived and, thus, can speed up real-time processing.