Discovering High-Order Periodic Patterns

Abstract

Discovery of periodic patterns in time series data has become an active research area with many applications. These patterns can be hierarchical in nature, where a higher-level pattern may consist of repetitions of lower-level patterns. Unfortunately, the presence of noise may prevent these higher-level patterns from being recognized in the sense that two portions (of a data sequence) that support the same (high-level) pattern may have different layouts of occurrences of basic symbols. There may not exist any common representation in terms of raw symbol combinations; and hence such (high-level) pattern may not be expressed by any previous model (defined on raw symbols or symbol combinations) and would not be properly recognized by any existing method. In this paper, we propose a novel model, namely meta-pattern, to capture these high-level patterns. As a more flexible model, the number of potential meta-patterns could be very large. A substantial difficulty lies in how to identify the proper pattern candidates. However, the well-known Apriori property is not able to provide sufficient pruning power. A new property, namely component location property, is identified and used to conduct the candidate generation so that an efficient computation-based mining algorithm can be developed. Last, but not least, we apply our algorithm to some real and synthetic sequences and some interesting patterns are discovered.