New Algorithm Speeds Partial Optimal Transport on Circles

Soheil Kolouri· August 26, 2026 View original

Key takeaways

  • PAWC offers an O(N log N) solution for partial optimal transport on circular data.
  • It significantly improves robustness to outliers, occlusion, and clutter.
  • The algorithm efficiently computes the full profile of optimal costs for all transported masses.
  • It has broad applications for periodic data in various fields.

Who benefits

Computer VisionSignal ProcessingRoboticsHealthcareGeospatial

Summary

Researchers developed PAWC, an O(N log N) algorithm for partial optimal transport on circular data, significantly outperforming previous methods. This algorithm efficiently computes the entire profile of optimal costs for varying transported masses, making it robust to outliers and clutter in periodic data.

A new algorithm, PAWC (Partial Wasserstein on Circles), has been introduced to address the challenge of partial optimal transport on circular data. Unlike traditional optimal transport, partial optimal transport is designed to be robust against outliers, occlusion, and clutter by allowing a portion of the mass to remain unmatched. Previous methods for circular data were computationally intensive, scaling at O(N^2 log N). PAWC significantly improves this by achieving an O(N log N) time complexity and O(N) memory usage. It efficiently calculates the entire profile of optimal costs for all possible transported cardinalities in a single run. This breakthrough is particularly relevant for data types that are inherently periodic, such as angles, phases, and time of day. Empirical results demonstrate PAWC's superior performance in speed and accuracy, especially in scenarios with occluded or cluttered data, and its applicability extends to higher-dimensional spheres.

Why it matters

This advancement provides a much faster and more robust method for comparing periodic data distributions, which is crucial for applications in computer vision, signal processing, and any domain dealing with circular or angular measurements. Its efficiency makes it practical for large-scale datasets and real-time applications.

How to implement this in your domain

  1. 1Integrate the PAWC algorithm into existing data analysis pipelines that handle periodic data.
  2. 2Evaluate PAWC's performance on current datasets where traditional optimal transport struggles with outliers.
  3. 3Explore applying PAWC to new problems involving angular or directional data in machine learning models.
  4. 4Utilize the provided code repository to experiment with the algorithm's capabilities.

Original post by Soheil Kolouri

"arXiv:2608.23910v1 Announce Type: new Abstract: Partial optimal transport compares two measures while leaving part of the mass unmatched, which is what makes it robust to outliers, occlusion, and clutter. The quantity of interest is usually the whole profile - the optimal cost at…"

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