Scalable Gromov-Wasserstein Based Comparison of Biological Time Series

Area of Science:

• Computational Biology
• Data Science
• Biophysics

Background:

• Time series data are abundant in biological research.
• Comparing these time series requires accurate and efficient distance measures.
• Existing methods face challenges with varying data dimensions and spacing.

Purpose of the Study:

• To introduce a new optimal transport-based distance for comparing biological time series.
• To address challenges posed by differing dimensions, point numbers, and spacing in trajectories.
• To provide a fast, scalable, and accurate method for time series analysis in biology.

Main Methods:

• Developed a modified Gromov-Wasserstein distance optimization program.
• Reduced the problem to a one-dimensional Wasserstein distance for computational efficiency.
• Utilized Fused Gromov-Wasserstein barycenters for averaging oscillatory time series.

Main Results:

• The proposed distance offers a closed-form solution computable with high speed.
• Empirical evaluations demonstrate strong performance on diverse biological datasets.
• Averaging using Fused Gromov-Wasserstein barycenters preserves more trajectory characteristics than traditional methods.

Conclusions:

• The new distance measure enables fast and meaningful comparisons of biological time series.
• It is applicable to a wide range of biological data analysis tasks.
• The method offers significant advantages for analyzing complex biological dynamics.