  When applying principal component analysis (PCA) for dimension reduction, the
most varying projections are usually used in order to retain most of the
information. For the purpose of anomaly and change detection, however, the
least varying projections are often the most important ones. In this article,
we present a novel method that automatically tailors the choice of projections
to monitor for sparse changes in the mean and/or covariance matrix of
high-dimensional data. A subset of the least varying projections is almost
always selected based on a criteria of the projection's sensitivity to changes.
  Our focus is on online/sequential change detection, where the aim is to
detect changes as quickly as possible, while controlling false alarms at a
specified level. A combination of tailored PCA and a generalized log-likelihood
monitoring procedure displays high efficiency in detecting even very sparse
changes in the mean, variance and correlation. We demonstrate on real data that
tailored PCA monitoring is efficient for sparse change detection also when the
data streams are highly auto-correlated and non-normal. Notably, error control
is achieved without a large validation set, which is needed in most existing
methods.
