An Empirical Evaluation of Time-Series Feature Sets

Solving time-series problems using informative features has been rising in popularity due to the availability of numerous software packages for time-series feature extraction. Feature-based time-series analysis can now be performed using any one of a range of time-series feature sets, including hctsa (7730 features: Matlab), feasts (42 features: R), tsfeatures (63 features: R), Kats (40 features: Python), tsfresh (up to 1558 features: Python), TSFEL (390 features: Python), and the C-coded catch22 (22 features, able to be run from Matlab, R, Python, and Julia). There is substantial overlap in the types of time-series analysis methods included in these feature sets (including properties of the autocorrelation function and Fourier power spectrum, and distributional shape statistics), but they are yet to be systematically compared. Here we compare these seven feature sets on their computational speed, assess the redundancy of features contained in each set, and evaluate the overlap and redundancy across different feature sets. We take an empirical approach to measuring feature similarity, based on the similarity of their outputs across a diverse set of real-world and model-simulated time series. We find that feature sets vary across approximately three orders of magnitude in their computation time per feature on a laptop for a 1000-sample time series, from the fastest feature sets catch22 and TSFEL (∼ 0.1 ms per feature) to tsfeatures (∼ 3 s per feature). Using PCA to evaluate feature redundancy within each set, we find the highest within-set redundancy for TSFEL and tsfresh. For example, in TSFEL, 90% of the variance across 390 features can be captured with just four principal components. Finally, we introduce a metric for quantifying overlap between pairs of feature sets, which indicates substantial overlap between the feature sets. We found that the largest feature set, hctsa, is the most comprehensive, and that tsfresh is the most distinctive, due to its incorporation of large numbers of Fourier coefficients that are summarized at higher levels in the other sets. Our results provide empirical understanding of the differences between existing feature sets, information that can be used to better understand and tailor feature sets to their applications.