Bidirectional piecewise linear representation of time series with application to collective anomaly detection

Directly mining high-dimensional time series presents several challenges, such as time and space costs. This study proposes a new approach for representing time series data and evaluates its effectiveness in detecting collective anomalies. The proposed method, called bidirectional piecewise linear representation (BPLR), represents the original time series using a set of linear fitting functions, which allows for dimensionality reduction while maintaining its dynamic characteristics. Similarity measurement is then performed using the piecewise integration (PI) approach, which achieves good detection performance with low computational overhead. Experimental results on synthetic and real-world data sets confirm the effectiveness and advantages of the proposed approach. The ability of the proposed method to capture more dynamic details of time series leads to consistently superior performance compared to other existing methods.