  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.
