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, such as Euclidean distance. However, in many cases there may not exist a single dissimilarity measure that captures all possible anomalous patterns. In such a case, multiple criteria can be defined, and one can test for anomalies by scalarizing the multiple criteria using a linear combination of them. 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. 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 and is provably better than linear combinations of the criteria.

💡 Research Summary

The paper addresses the limitation of most anomaly‑detection methods that rely on a single dissimilarity measure. In many real‑world scenarios multiple criteria (e.g., speed, shape, color) are needed to capture the full spectrum of anomalous behavior, but combining them via a weighted linear sum requires prior knowledge of the weights and repeated executions for different weight choices. To overcome this, the authors propose a novel non‑parametric multi‑criteria anomaly‑detection framework called Pareto Depth Analysis (PDA).

The core idea is to represent every pair of data points (i, j) by a K‑dimensional “dyad” D₍ᵢⱼ₎ =