  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.
