An Efficient Method for Estimating Time Series Motif Length Using Sequitur Algorithm

Abstract

Motifs in time series are approximately repeated subsequence found within a long time series data. There are some popular and effective algorithms for finding motif in time series. However, these algorithms still have one major weakness: users of these algorithms are required to select an appropriate value of the motif length which is unknown in advance. In this paper, we propose a novel method to estimate the length of 1-motif in a time series. This method is based on GrammarViz, a variable-length motif detection approach which has Sequitur at its core. Sequitur is known as a grammar compression algorithm that is able to have enough identification not just common subsequences but also identify the hierarchical structure in data. As GrammarViz, our method is also based on the Sequitur algorithm, but for another purpose: a preprocessing step for finding motif in time series. The experimental results prove that our method can help to estimate very fast the length of 1-motif for some TSMD algorithms, such as Random Projection.