Which principal components are most sensitive to distributional changes?
This provides a theoretical basis for improving anomaly detection in high-dimensional data, though it is incremental as it builds on existing PCA methods.
The paper tackled the problem of identifying which principal components are most sensitive to distributional changes for anomaly detection, proving that the minor projection is most sensitive in bivariate data and showing simulations extend this to higher dimensions.
PCA is often used in anomaly detection and statistical process control tasks. For bivariate 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 by the Hellinger distance between distributions before and after a change. In particular, this is almost always the case if only one parameter of the bivariate normal distribution changes, i.e., 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. This motivates using the minor projections for detecting sparse distributional changes in high-dimensional data.