Anomaly detection using principles of human perception

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.