Data driven structural similarity: A Distance measure for adaptive linear approximations of time series

Much effort has been invested in recent years in the problem of detecting similarity in time series. Most work focuses on the identification of exact matches through point-by-point comparisons, although in many real-world problems recurring patterns match each other only approximately. We introduce a new approach for identifying patterns in time series, which evaluates the similarity by comparing the overall structure of candidate sequences instead of focusing on the local shapes of the sequence and propose a new distance measure ABC (Area Between Curves) that is used to achieve this goal. The approach is based on a data-driven linear approximation method that is intuitive, offers a high compression ratio and adapts to the overall shape of the sequence. The similarity of candidate sequences is quantified by means of the novel distance measure, applied directly to the linear approximation of the time series. Our evaluations performed on multiple data sets show that our proposed technique outperforms similarity search approaches based on the commonly referenced Euclidean Distance in the majority of cases. The most significant improvements are obtained when applying our method to domains and data sets where matching sequences are indeed primarily determined based on the similarity of their higher-level structures.