  Solving time-series problems with features has been rising in popularity due
to the availability of software for feature extraction. Feature-based
time-series analysis can now be performed using many different 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:
Matlab, R, Python, and Julia). There is substantial overlap in the types of
methods included in these sets (e.g., properties of the autocorrelation
function and Fourier power spectrum), but they are yet to be systematically
compared. Here we compare these seven sets on computational speed, assess the
redundancy of features contained in each, and evaluate the overlap and
redundancy between them. We take an empirical approach to feature similarity
based on outputs across a diverse set of real-world and simulated time series.
We find that feature sets vary across three orders of magnitude in their
computation time per feature on a laptop for a 1000-sample series, from the
fastest sets catch22 and TSFEL (~0.1ms per feature) to tsfeatures (~3s 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 PCs.
Finally, we introduce a metric for quantifying overlap between pairs of feature
sets, which indicates substantial overlap. We found that the largest feature
set, hctsa, is the most comprehensive, and that tsfresh is the most
distinctive, due to its incorporation of many low-level Fourier coefficients.
Our results provide empirical understanding of the differences between existing
feature sets, information that can be used to better tailor feature sets to
their applications.
