IterativE Grammar-Based Framework for Discovering Variable-Length Time Series Motifs

In recent years, finding repetitive similar patterns in time series has become a popular problem. These patterns are called time series motifs. Recent studies show that using grammar compression algorithms to find repeating patterns from the symbolized time series holds promise in discovering approximate motifs with variable length. However, grammar compression algorithms are traditionally designed for string compression. Therefore, existing work on grammar induction has not fully utilized much available information that can be used to enhance the performance of the algorithms. In this work, an iterative framework based on grammar induction is proposed. In each iteration, a revision operator called Noise Reduction Operator is applied to revise the symbolized time series string based on the rules returned from a base grammar induction algorithm. In our experiments, we show that the proposed work can find motifs of the same quality, with much faster running time compared to the state-of-the-art variable-length exact motif discovery algorithm in real world time series data.