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Mining periodic patterns in time series databases is an important data mining problem with many applications. Previous studies have considered synchronous periodic patterns where misaligned occurrences are not allowed. However, asynchronous periodic pattern mining has received less attention and only been discussed for a sequence of symbols where each time point contains one event. In this paper, we propose a more general model of asynchronous periodic patterns from a sequence of symbol sets where a time slot can contain multiple events. Three parameters min\_rep, max\_dis, and global\_rep are employed to specify the minimum number of repetitions required for a valid segment of nondisrupted pattern occurrences, the maximum allowed disturbance between two successive valid segments, and the total repetitions required for a valid sequence. A 4-phase algorithm is devised to discover periodic patterns from a time series database presented in vertical format. The experiments demonstrate good performance and scalability with large frequent patterns.
Periodic pattern, asynchronous sequence, partial periodicity, temporal database.

C. Chang and K. Huang, "SMCA: A General Model for Mining Asynchronous Periodic Patterns in Temporal Databases," in IEEE Transactions on Knowledge & Data Engineering, vol. 17, no. , pp. 774-785, 2005.
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