  In the fields of statistics and unsupervised machine learning a fundamental
and well-studied problem is anomaly detection. Although anomalies are difficult
to define, 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 gives a philosophical approach to
clearly define anomalies and to develop an algorithm for their efficient
detection with minimal user intervention. Inspired by the Gestalt School of
Psychology and the Helmholtz principle of human perception, the idea is to
assume anomalies are observations that are unexpected to occur with respect to
certain groupings made by the majority of the data. Thus, under appropriate
random variable modelling anomalies are directly found in a set of data under a
uniform and independent random assumption of the distribution of constituent
elements of the observations; anomalies correspond to those observations where
the expectation of occurrence 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 the prime choice for univariate data and it shows
promising performance on the detection of global anomalies in multivariate
data.
