Which principal components are most sensitive in the change detection problem?

Abstract

Principal component analysis (PCA) is often used in anomaly detection and statistical process control tasks. For bivariate normal data, we prove that the minor projection (the least varying projection) of the PCA‐rotated data is the most sensitive to distributional changes, where sensitivity is defined as the Hellinger distance between the projections' marginal distributions before and after a change. In particular, this is almost always the case if only one parameter of the bivariate normal distribution changes, that is, the change is sparse. Simulations indicate that the minor projections are the most sensitive for a large range of changes and pre‐change settings in higher dimensions as well, including changes that are very sparse. This motivates using only a few of the minor projections for detecting sparse distributional changes in high‐dimensional data.

Nonstationarity in correlation matrices for wind turbine SCADA‐data

“…They are commonly applied to wind turbines, 11,19,24–26,63 see also the reviews mentioned in the introduction. We have recently shown that for generic correlated systems with distinct normal states, the knowledge of these states increases the sensitivity of change detection based on principal components 36,37 . This is possible via pre‐processing: Using a criterion based on historical data—wind speed in the presented case—new or live data could be compared to the respective operational states.…”

“…We have recently shown that for generic correlated systems with distinct normal states, the knowledge of these states increases the sensitivity of change detection based on principal components. 36,37 This is possible via pre-processing: Using a criterion based on historical data-wind speed in the presented case-new or live data could be compared to the respective operational states. Charmingly, the proposed ansatz does not require changes in established techniques, it just requires their application to multiple subgroups and is therefore easily implemented.…”

“…Such nonstationarity is important also in many applications aside from wind turbines 30–35 . We have recently shown that nonstationarity in correlated systems is important for the detection of anomalies 36,37 . For wind turbines, it has been shown to have an effect on failure detection 38,39 .…”

“…[30][31][32][33][34][35] We have recently shown that nonstationarity in correlated systems is important for the detection of anomalies. 36,37 For wind turbines, it has been shown to have an effect on failure detection. 38,39 Furthermore, different states in frequency data measured by a CMS system have been identified due to operational regimes.…”

Determining the number of change‐point via high‐dimensional cross‐validation

“…Change‐point detection has recently attracted enormous attention due to the rapid changes and developments in the era of big data, where heterogeneity is one of the most commonly encountered issues (Baranowski et al, ; Chiou et al, ; Eichinger & Kirch, ; Fryzlewicz, ; Banerjee & Guhathakurta, ). Change‐point detection is the process of detecting changes in the underlying model, including changes in mean, variance, or distribution, from a time‐ordered sequence of observations (Banerjee & Guhathakurta, ; Tveten, ). Numerous change‐point detection methods have been developed recently (Arlot et al, ; Dubey & Müller, ; Killick et al, ; Padilla et al, ; Wang et al, ; Zhang & Siegmund, ).…”