Scalable Gromov-Wasserstein Based Comparison of Biological Time Series

by Natalia Kravtsova, Reginald L McGee and Adriana T Dawes

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In this paper, we introduce a rigorous and powerful method for comparing time series data using a novel and computationally efficient modification of the Gromov-Wasserstein optimal transport distance. In brief, our method, which we denote GW$_{\tau}$, views each trajectory as a separate metric space and compares these metric spaces via optimal transport. This feature of our method makes it exceptionally flexible in the types and size of data sets that can be compared, including data sets that occur on different time scales, are missing measurements, or even lie in spaces of different dimensions. Its rigorously demonstrated properties show a clear increase in efficiency and accuracy over other methods and using a variety of data. Using our method, we show that averaging time series using recently proposed Fused Gromov-Wasserstein barycenters provides more reliable average trajectories compared to the most commonly used mean trajectories. Our easily implemented and fast GW$_{\tau}$ method can be applied to a wide range of time series data, from cell biology to ecology, and allows for new comparisons and quantifications that preserve key features in the data sets.

Natalia Kravtsova, a student author, led the research in this paper, including formal analysis, methodology, and visualization. Prof. McGee and Prof. Dawes provided supervision. All three authors contributed to the formulation and conceptualization of the research, and manuscript preparation.