Very large time series are increasingly available from an ever wider range of IoT-enabled sensors deployed in different environments. Significant insights can be obtained through mining temporal patterns from these time series. Unlike traditional pattern mining, temporal pattern mining (TPM) adds additional temporal aspect  into extracted patterns, thus making them more expressive. However, adding the temporal dimension into patterns results in an exponential growth of the search space, significantly increasing the mining process complexity. Current TPM approaches either cannot scale to large datasets, or typically work on pre-processed event sequences rather than directly on time series. This paper presents our comprehensive Frequent Temporal Pattern Mining from Time Series (FTPMfTS) approach which provides the following contributions: (1) The end-to-end FTPMfTS process that directly takes time series as input and produces frequent temporal patterns as output. (2) The efficient Hierarchical Temporal Pattern Graph Mining (HTPGM) algorithm that uses efficient data structures to enable fast computations for support and confidence . (3) A number of pruning techniques for HTPGM that yield significantly faster mining. ( 4 ) An approximate version of HTPGM which relies on mutual information to prune unpromising time series, and thus significantly reduce the search space. ( 5 ) An extensive experimental evaluation on  real-world datasets from the energy and smart city domains which shows that HTPGM outperforms the baselines and can scale to large datasets. The approximate HTPGM achieves up to 3 orders of magnitude speedup compared to the baselines and consumes significantly less memory, while obtaining high accuracy compared to the exact HTPGM.
Very large time series are increasingly available from an ever wider range of IoT-enabled sensors deployed in different environments. Significant insights can be obtained through mining temporal patterns from these time series. Unlike traditional pattern mining, temporal pattern mining (TPM) adds additional temporal aspect , e.g., the time intervals of the events, into extracted patterns, making them more expressive. However, adding this extra temporal information to the patterns also adds an additional exponential factor to the exponential growth of the search space, increases significantly the mining complexity. This raises an imperative need to have a more efficient and scalable method for temporal pattern mining. Existing TPM methods either cannot scale to large datasets, or work only on pre-processed temporal events rather than on time series. This paper presents our comprehensive Frequent Temporal Pattern Mining from Time Series (FTPMfTS) with the following contributions: (1) The end-to-end FTPMfTS process that directly takes time series as input and produces frequent temporal patterns as output. (2) The efficient Hierarchical Temporal Pattern Graph Mining (HTPGM) algorithm that uses efficient data structures to enable fast computations of support and confidence , and employs effective pruning techniques to achieve significantly faster mining. ( 3 ) An approximate version of HTPGM which relies on mutual information to prune unpromising time series, and thus significantly reduce the search space. ( 4 ) An extensive experimental evaluation on synthetic and real-world datasets shows that HTPGM outperforms the baselines in runtime and memory consumption, and can scale to big datasets. The approximate HTPGM achieves up to 2 orders of magnitude speedup compared to the baselines while having high accuracy compared to the exact HTPGM.
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