Multi-criteria Similarity-based Anomaly Detection using Pareto Depth Analysis

TL;DR

This paper introduces a novel Pareto depth-based method for anomaly detection that effectively integrates multiple dissimilarity measures without needing multiple runs or weight tuning, outperforming traditional linear combination approaches.

Contribution

The paper proposes the Pareto depth analysis (PDA) algorithm, a new multi-criteria anomaly detection method leveraging Pareto optimality to improve detection accuracy.

Findings

PDA outperforms linear combination methods in experiments.

The approach is effective with synthetic and real datasets.

PDA avoids multiple runs with different weights.

Abstract

We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. Similarity-based anomaly detection algorithms detect abnormally large amounts of similarity or dissimilarity, e.g.~as measured by nearest neighbor Euclidean distances between a test sample and the training samples. In many application domains there may not exist a single dissimilarity measure that captures all possible anomalous patterns. In such cases, multiple dissimilarity measures can be defined, including non-metric measures, and one can test for anomalies by scalarizing using a non-negative linear combination of them. If the relative importance of the different dissimilarity measures are not known in advance, as in many anomaly detection applications, the anomaly detection algorithm may need to be executed multiple times with different choices of weights in the linear combination. In this paper, we propose a method for similarity-based anomaly detection using a novel multi-criteria dissimilarity measure, the Pareto depth. The proposed Pareto depth analysis (PDA) anomaly detection algorithm 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 is provably better than using linear combinations of the criteria and shows superior performance on experiments with synthetic and real data sets.