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We combine the metrics of distance and isolation to develop the AnalyticIsolation and Distance-based Anomaly (AIDA) detection algorithm. AIDA is thefirst distance-based method that does not rely on the concept ofnearest-neighbours, making it a parameter-free model.  Differently from the prevailing literature, in which the isolation metric isalways computed via simulations, we show that AIDA admits an analyticalexpression for the outlier score, providing new insights into the isolationmetric. Additionally, we present an anomaly explanation method based on AIDA,the Tempered Isolation-based eXplanation (TIX) algorithm, which finds the mostrelevant outlier features even in data sets with hundreds of dimensions. Wetest both algorithms on synthetic and empirical data: we show that AIDA iscompetitive when compared to other state-of-the-art methods, and it is superiorin finding outliers hidden in multidimensional feature subspaces. Finally, weillustrate how the TIX algorithm is able to find outliers in multidimensionalfeature subspaces, and use these explanations to analyze common benchmarks usedin anomaly detection.

AIDA: Analytic Isolation and Distance-based Anomaly Detection Algorithm