Multi-criteria Anomaly Detection using Pareto Depth Analysis

We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. In most anomaly detection algorithms, the dissimilarity between data samples is calculated by a single criterion. When dissimilarities are calculated by multiple criteria, one might perform anomaly detection using a linear combination of the multiple dissimilarities. If the importance of the different criteria are not known in advance, the algorithm may need to be executed multiple times with different choices of weights in the linear combination, perhaps selected by grid search. In this paper, we introduce a novel non-parametric multi-criteria anomaly detection method using Pareto depth analysis (PDA). PDA uses the concept of Pareto optimality to detect anomalies under multiple criteria without having to run an algorithm multiple times with different choices of weights. The proposed PDA approach scales linearly in the number of criteria, unlike grid search methods, which scale exponentially. We find that PDA is able to outperform any linear combination of criteria, including weights selected by grid search.