  Nearest-neighbor (NN) procedures are well studied and widely used in both
supervised and unsupervised learning problems. In this paper we are concerned
with investigating the performance of NN-based methods for anomaly detection.
We first show through extensive simulations that NN methods compare favorably
to some of the other state-of-the-art algorithms for anomaly detection based on
a set of benchmark synthetic datasets. We further consider the performance of
NN methods on real datasets, and relate it to the dimensionality of the
problem. Next, we analyze the theoretical properties of NN-methods for anomaly
detection by studying a more general quantity called distance-to-measure (DTM),
originally developed in the literature on robust geometric and topological
inference. We provide finite-sample uniform guarantees for the empirical DTM
and use them to derive misclassification rates for anomalous observations under
various settings. In our analysis we rely on Huber's contamination model and
formulate mild geometric regularity assumptions on the underlying distribution
of the data.
