  Currently, discovering subsequence anomalies in time series remains one of
the most topical research problems. A subsequence anomaly refers to successive
points in time that are collectively abnormal, although each point is not
necessarily an outlier. Among a large number of approaches to discovering
subsequence anomalies, the discord concept is considered one of the best. A
time series discord is intuitively defined as a subsequence of a given length
that is maximally far away from its non-overlapping nearest neighbor. Recently
introduced the MERLIN algorithm discovers time series discords of every
possible length in a specified range, thereby eliminating the need to set even
that sole parameter to discover discords in a time series. However, MERLIN is
serial and its parallelization could increase the performance of discords
discovery. In this article, we introduce a novel parallelization scheme for
GPUs, called PALMAD, Parallel Arbitrary Length MERLIN-based Anomaly Discovery.
As opposed to its serial predecessor, PALMAD employs recurrent formulas we have
derived to avoid redundant calculations, and advanced data structures for the
efficient implementation of parallel processing. Experimental evaluation over
real-world and synthetic time series shows that our algorithm outperforms
parallel analogs. We also apply PALMAD to discover anomalies in a real-world
time series employing our proposed discord heatmap technique to illustrate the
results.
