Highly comparative time-series analysis: the empirical structure of time series and their methods

Abstract

The process of collecting and organizing sets of observations represents a common theme throughout the history of science. However, despite the ubiquity of scientists measuring, recording and analysing the dynamics of different processes, an extensive organization of scientific time-series data and analysis methods has never been performed. Addressing this, annotated collections of over 35 000 real-world and model-generated time series, and over 9000 time-series analysis algorithms are analysed in this work. We introduce reduced representations of both time series, in terms of their properties measured by diverse scientific methods, and of time-series analysis methods, in terms of their behaviour on empirical time series, and use them to organize these interdisciplinary resources. This new approach to comparing across diverse scientific data and methods allows us to organize time-series datasets automatically according to their properties, retrieve alternatives to particular analysis methods developed in other scientific disciplines and automate the selection of useful methods for time-series classification and regression tasks. The broad scientific utility of these tools is demonstrated on datasets of electroencephalograms, self-affine time series, heartbeat intervals, speech signals and others, in each case contributing novel analysis techniques to the existing literature. Highly comparative techniques that compare across an interdisciplinary literature can thus be used to guide more focused research in time-series analysis for applications across the scientific disciplines.

Scattering Transform for Intrapartum Fetal Heart Rate Variability Fractal Analysis: A Case-Control Study

“…A large database should permit to address two issues: How can the individual classificationpower of various features be compared (cf. [6], [30]) ? How should supervised classification strategies (relying on sets of selected features) be implemented and compared ?…”

Structural connectome topology relates to regional BOLD signal dynamics in the mouse brain

“…We correct for 6930 independent tests, even though there are only approximately 200 linearly independent time-series behaviors in our feature set due to the existence of highly correlated time-series features, cf. Fulcher et al 32 Our results thus constitute a highly conservative estimate of the number of time-series features that are significantly related to each topological quantity, minimizing the false positive rate (type I error) at the cost of increasing the false negative rate (type II error). In the absence of such a strong signal, future work could use multivariate methods (such as canonical correlation analysis or partial least squares) to find informative component-wise relationships between the two types of data.…”

“…Rather than manually selecting a small number of such time-series features, here we aimed to determine the most informative features for understanding structural connectivity properties in a purely data-driven way. To achieve this, we used the highly comparative timeseries analysis software package, hctsa (v0.91, github.com/ benfulcher/hctsa) 32,33,46 to extract a total of 7754 informative features from each of the 3312 BOLD time series in our dataset (cf. Fig.…”

“…31 However, quite apart from properties of the power spectrum, thousands of alternative time-series analysis methods exist that might contain useful information, such as those developed for applications in statistics, electrical engineering, economics, statistical physics, dynamical systems, and biomedicine. 32 Here we leverage this vast interdisciplinary library of time-series analysis methods to characterize the fluctuations of spontaneous regional activity using restingstate fMRI (rs-fMRI), applying a recently developed highly comparative analysis framework that extracts over 7700 properties from univariate time series. 32,33 In this way, we computed thousands of properties of the intrinsic rs-fMRI dynamics in each brain region using data from 18 anesthetized mice.…”

“…32 Here we leverage this vast interdisciplinary library of time-series analysis methods to characterize the fluctuations of spontaneous regional activity using restingstate fMRI (rs-fMRI), applying a recently developed highly comparative analysis framework that extracts over 7700 properties from univariate time series. 32,33 In this way, we computed thousands of properties of the intrinsic rs-fMRI dynamics in each brain region using data from 18 anesthetized mice. Structural network connectivity properties of each brain region were also computed using a mesoscale mouse connectome estimated from viral tract-tracing experiments.…”