  A time series is a collection of measurements in chronological order.
Discovering patterns from time series is useful in many domains, such as stock
analysis, disease detection, and weather forecast. To discover patterns,
existing methods often convert time series data into another form, such as
nominal/symbolic format, to reduce dimensionality, which inevitably deviates
the data values. Moreover, existing methods mainly neglect the order
relationships between time series values. To tackle these issues, inspired by
order-preserving matching, this paper proposes an Order-Preserving sequential
Pattern (OPP) mining method, which represents patterns based on the order
relationships of the time series data. An inherent advantage of such
representation is that the trend of a time series can be represented by the
relative order of the values underneath the time series data. To obtain
frequent trends in time series, we propose the OPP-Miner algorithm to mine
patterns with the same trend (sub-sequences with the same relative order).
OPP-Miner employs the filtration and verification strategies to calculate the
support and uses pattern fusion strategy to generate candidate patterns. To
compress the result set, we also study finding the maximal OPPs. Experiments
validate that OPP-Miner is not only efficient and scalable but can also
discover similar sub-sequences in time series. In addition, case studies show
that our algorithms have high utility in analyzing the COVID-19 epidemic by
identifying critical trends and improve the clustering performance.
