Anomaly Detection Using Causal Sliding Windows

Anomaly detection using sliding windows is not new but using causal sliding windows has not been explored in the past. The need of causality arises from real-time processing where the used sliding windows should not include future data samples that have not been visited, i.e., data samples come in after the currently being processed data sample. This paper develops an approach to anomaly detection using causal sliding windows, which has the capability of being implemented in real time. In doing so, three types of causal windows are defined: 1) causal sliding square matrix windows; 2) causal sliding rectangular matrix windows; and 3) causal sliding array windows. By virtue of causal sliding windows, a causal sample covariance/correlation matrix can be derived for causal anomaly detection. As for the causal sliding array windows, recursive update equations are also derived and thus speed up real-time processing.