  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.
