  At the crossway of machine learning and data analysis, anomaly detection aims
at identifying observations that exhibit abnormal behaviour. Be it measurement
errors, disease development, severe weather, production quality default(s)
(items) or failed equipment, financial frauds or crisis events, their on-time
identification and isolation constitute an important task in almost any area of
industry and science. While a substantial body of literature is devoted to
detection of anomalies, little attention is payed to their explanation. This is
the case mostly due to intrinsically non-supervised nature of the task and
non-robustness of the exploratory methods like principal component analysis
(PCA).
  We introduce a new statistical tool dedicated for exploratory analysis of
abnormal observations using data depth as a score. Anomaly component analysis
(shortly ACA) is a method that searches a low-dimensional data representation
that best visualises and explains anomalies. This low-dimensional
representation not only allows to distinguish groups of anomalies better than
the methods of the state of the art, but as well provides a -- linear in
variables and thus easily interpretable -- explanation for anomalies. In a
comparative simulation and real-data study, ACA also proves advantageous for
anomaly analysis with respect to methods present in the literature.
