  In the fields of statistics and unsupervised machine learning a fundamental
and well-studied problem is anomaly detection. Anomalies are difficult to
define, yet many algorithms have been proposed. Underlying the approaches is
the nebulous understanding that anomalies are rare, unusual or inconsistent
with the majority of data. The present work provides a philosophical treatise
to clearly define anomalies and develops an algorithm for their efficient
detection with minimal user intervention. Inspired by the Gestalt School of
Psychology and the Helmholtz principle of human perception, anomalies are
assumed to be observations that are unexpected to occur with respect to certain
groupings made by the majority of the data. Under appropriate random variable
modelling anomalies are directly found in a set of data by a uniform and
independent random assumption of the distribution of constituent elements of
the observations, with anomalies corresponding to those observations where the
expectation of the number of occurrences of the elements in a given view is
$<1$. Starting from fundamental principles of human perception an unsupervised
anomaly detection algorithm is developed that is simple, real-time and
parameter-free. Experiments suggest it as a competing choice for univariate
data with promising results on the detection of global anomalies in
multivariate data.

Cryptography and Security;Machine Learning;Machine Learning