A Meta-Analysis of the Anomaly Detection Problem

Abstract

This article provides a thorough meta-analysis of the anomaly detection problem. To accomplish this we first identify approaches to benchmarking anomaly detection algorithms across the literature and produce a large corpus of anomaly detection benchmarks that vary in their construction across several dimensions we deem important to real-world applications: (a) point difficulty, (b) relative frequency of anomalies, (c) clusteredness of anomalies, and (d) relevance of features. We apply a representative set of anomaly detection algorithms to this corpus, yielding a very large collection of experimental results. We analyze these results to understand many phenomena observed in previous work. First we observe the effects of experimental design on experimental results. Second, results are evaluated with two metrics, ROC Area Under the Curve and Average Precision. We employ statistical hypothesis testing to demonstrate the value (or lack thereof) of our benchmarks. We then offer several approaches to summarizing our experimental results, drawing several conclusions about the impact of our methodology as well as the strengths and weaknesses of some algorithms. Last, we compare results against a trivial solution as an alternate means of normalizing the reported performance of algorithms. The intended contributions of this article are many; in addition to providing a large publicly-available corpus of anomaly detection benchmarks, we provide an ontology for describing anomaly detection contexts, a methodology for controlling various aspects of benchmark creation, guidelines for future experimental design and a discussion of the many potential pitfalls of trying to measure success in this field.