  Recognition of anomalous events is a challenging but critical task in many
scientific and industrial fields, especially when the properties of anomalies
are unknown. In this paper, we introduce a new anomaly concept called "unicorn"
or unique event and present a new, model-free, unsupervised detection algorithm
to detect unicorns. The key component of the new algorithm is the Temporal
Outlier Factor (TOF) to measure the uniqueness of events in continuous data
sets from dynamic systems. The concept of unique events differs significantly
from traditional outliers in many aspects: while repetitive outliers are no
longer unique events, a unique event is not necessarily an outlier; it does not
necessarily fall out from the distribution of normal activity. The performance
of our algorithm was examined in recognizing unique events on different types
of simulated data sets with anomalies and it was compared with the Local
Outlier Factor (LOF) and discord discovery algorithms. TOF had superior
performance compared to LOF and discord algorithms even in recognizing
traditional outliers and it also recognized unique events that those did not.
The benefits of the unicorn concept and the new detection method were
illustrated by example data sets from very different scientific fields. Our
algorithm successfully recognized unique events in those cases where they were
already known such as the gravitational waves of a binary black hole merger on
LIGO detector data and the signs of respiratory failure on ECG data series.
Furthermore, unique events were found on the LIBOR data set of the last 30
years.
