Discovering Periodicity in Locally Repeating Patterns

Analysing and learning from sequentially ordered symbolic data is increasingly important in applications such as finance and biology. Finding patterns that show interesting behaviour, such as regularly repeating occurrences within a time interval, can provide useful insight. In this paper we address the problem of efficiently identifying such behaviours. Existing approaches often require a target period to be specified, which will limit possible patterns to those approximating the specified periodicity, such as daily, monthly, quarterly and so on. In this paper we extend one such approach, derived from frequent pattern mining, to operate without the need for user-specified periodicity. Our new algorithms can identify the time interval and periodicity, or frequency of occurrence, of all periodically occurring patterns within a certain used-specified tolerance. Experimental results of our implementation show that the new approach can identify many more patterns in a real-world financial dataset, while on other sequential datasets it finds similar numbers of patterns without significant reduction in efficiency compared to existing approaches. We also verify the algorithm's ability to recover recurring patterns in controlled experiments on synthetic data.