  Discovering frequent trends in time series is a critical task in data mining.
Recently, order-preserving matching was proposed to find all occurrences of a
pattern in a time series, where the pattern is a relative order (regarded as a
trend) and an occurrence is a sub-time series whose relative order coincides
with the pattern. Inspired by the order-preserving matching, the existing
order-preserving pattern (OPP) mining algorithm employs order-preserving
matching to calculate the support, which leads to low efficiency. To address
this deficiency, this paper proposes an algorithm called efficient frequent OPP
miner (EFO-Miner) to find all frequent OPPs. EFO-Miner is composed of four
parts: a pattern fusion strategy to generate candidate patterns, a matching
process for the results of sub-patterns to calculate the support of
super-patterns, a screening strategy to dynamically reduce the size of prefix
and suffix arrays, and a pruning strategy to further dynamically prune
candidate patterns. Moreover, this paper explores the order-preserving rule
(OPR) mining and proposes an algorithm called OPR-Miner to discover strong
rules from all frequent OPPs using EFO-Miner. Experimental results verify that
OPR-Miner gives better performance than other competitive algorithms. More
importantly, clustering and classification experiments further validate that
OPR-Miner achieves good performance.
