Feature identification in time series data sets

Shaw, Justin; Stastna, Marek; Coutino, Aaron; Walter, Ryan; Reinhardt, Eduard G.

doi:10.1016/j.heliyon.2019.e01708

Cited by 2 publications

(1 citation statement)

References 17 publications

(26 reference statements)

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“…In the case of CFD data sets, this typically means many domain snapshots of a single physical field. We also recently published the γ method [36], which was designed primarily to find features in data sets consisting of time series sampling multiple physical fields. Together these two methods allow the quick identification of interesting features in a wide variety of data sets.…”

Section: Discussionmentioning

confidence: 99%

Feature identification in time-indexed model output

Shaw

Stastna

2019

PLoS ONE

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We present a method for identifying features (time periods of interest) in data sets consisting of time-indexed model output. The method is used as a diagnostic to quickly focus the attention on a subset of the data before further analysis methods are applied. Mathematically, the infinity norm errors of empirical orthogonal function (EOF) reconstructions are calculated for each time output. The result is an EOF reconstruction error map which clearly identifies features as changes in the error structure over time. The ubiquity of EOF-type methods in a wide range of disciplines reduces barriers to comprehension and implementation of the method. We apply the error map method to three different Computational Fluid Dynamics (CFD) data sets as examples: the development of a spontaneous instability in a large amplitude internal solitary wave, an internal wave interacting with a density profile change, and the collision of two waves of different vertical mode. In all cases the EOF error map method identifies relevant features which are worthy of further study.

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Section: Discussionmentioning

confidence: 99%

Feature identification in time-indexed model output

Shaw

Stastna

2019

PLoS ONE

Self Cite

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Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories

et al. 2021

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Extensive time-series encoding the position of particles such as viruses, vesicles, or individual proteins are routinely garnered in single-particle tracking experiments or supercomputing studies. They contain vital clues on how viruses spread or drugs may be delivered in biological cells. Similar time-series are being recorded of stock values in financial markets and of climate data. Such time-series are most typically evaluated in terms of time-averaged mean-squared displacements (TAMSDs), which remain random variables for finite measurement times. Their statistical properties are different for different physical stochastic processes, thus allowing us to extract valuable information on the stochastic process itself. To exploit the full potential of the statistical information encoded in measured time-series we here propose an easy-to-implement and computationally inexpensive new methodology, based on deviations of the TAMSD from its ensemble average counterpart. Specifically, we use the upper bound of these deviations for Brownian motion (BM) to check the applicability of this approach to simulated and real data sets. By comparing the probability of deviations for different data sets, we demonstrate how the theoretical bound for BM reveals additional information about observed stochastic processes. We apply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracer beads measured in mucin hydrogels, and of geographic surface temperature anomalies. Our analysis shows how the large-deviation properties can be efficiently used as a simple yet effective routine test to reject the BM hypothesis and unveil relevant information on statistical properties such as ergodicity breaking and short-time correlations.

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Feature identification in time series data sets

Cited by 2 publications

References 17 publications

Feature identification in time-indexed model output

Feature identification in time-indexed model output

Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories

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