Sensitivity of principal components to system changes in the presence of non-stationarity

TL;DR

This paper investigates how non-stationarity impacts the sensitivity of principal component-based change detection in correlated systems, demonstrating that knowledge of non-stationarity significantly enhances detection performance.

Contribution

It introduces a model of non-stationarity as multiple normal states and compares change detection sensitivity with and without this knowledge across various system configurations.

Findings

Knowledge of non-stationarity improves change detection sensitivity across all principal components.

The greatest sensitivity gains are observed in components already effective in stationary conditions.

Real traffic data analysis confirms the effectiveness of incorporating non-stationarity information.

Abstract

Non-stationarity affects the sensitivity of change detection in correlated systems described by sets of measurable variables. We study this by projecting onto different principal components. Non-stationarity is modeled as multiple normal states that exist in the system even before a change occurs. The studied changes occur in mean values, standard deviations or correlations of the variables. Monte Carlo simulations are performed to test the sensitivity for change detection with and without knowledge about the non-stationarity for different system dimensions and numbers of normal states. A comparison clearly shows that the knowledge about the non-stationarity of the system greatly improves change detection sensitivity for all principal components. This improvement is largest for those components that already provide the greatest possibility for change detection in the stationary case. We illustrate our results with an example using real traffic flow data, in which we detect a weekend and a bank holiday start as anomalies.