  Recently, order-preserving pattern (OPP) mining has been proposed to discover
some patterns, which can be seen as trend changes in time series. Although
existing OPP mining algorithms have achieved satisfactory performance, they
discover all frequent patterns. However, in some cases, users focus on a
particular trend and its associated trends. To efficiently discover trend
information related to a specific prefix pattern, this paper addresses the
issue of co-occurrence OPP mining (COP) and proposes an algorithm named
COP-Miner to discover COPs from historical time series. COP-Miner consists of
three parts: extracting keypoints, preparation stage, and iteratively
calculating supports and mining frequent COPs. Extracting keypoints is used to
obtain local extreme points of patterns and time series. The preparation stage
is designed to prepare for the first round of mining, which contains four
steps: obtaining the suffix OPP of the keypoint sub-time series, calculating
the occurrences of the suffix OPP, verifying the occurrences of the keypoint
sub-time series, and calculating the occurrences of all fusion patterns of the
keypoint sub-time series. To further improve the efficiency of support
calculation, we propose a support calculation method with an ending strategy
that uses the occurrences of prefix and suffix patterns to calculate the
occurrences of superpatterns. Experimental results indicate that COP-Miner
outperforms the other competing algorithms in running time and scalability.
Moreover, COPs with keypoint alignment yield better prediction performance.
