Summary of Partial Gromov-wasserstein Metric, by Yikun Bai et al.
Partial Gromov-Wasserstein Metric
by Yikun Bai, Rocio Diaz Martin, Abihith Kothapalli, Hengrong Du, Xinran Liu, Soheil Kolouri
First submitted to arxiv on: 6 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A new machine learning approach proposes a Partial Gromov-Wasserstein (PGW) distance that overcomes limitations of classical Gromov-Wasserstein distances by allowing for unbalanced comparisons between metric measure spaces. This PGW distance is shown to be a well-defined metric with theoretical properties, including the existence of a minimizer and relationships with GW distances. The authors also develop two variants of the Frank-Wolfe algorithm for solving the PGW problem, which are mathematically and computationally equivalent. Furthermore, they introduce the concept of barycenters for metric measure spaces based on this new distance. The effectiveness of PGW is demonstrated in applications such as shape matching, retrieval, and interpolation, outperforming existing baselines. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A new way to compare shapes and measures has been developed! Imagine you have different ways of measuring things, like inches or centimeters, and you want to find the closest match between two shapes. The Gromov-Wasserstein distance is a popular tool for doing this, but it only works when both shapes are the same size. What if they’re not? That’s where the new Partial Gromov-Wasserstein (PGW) distance comes in! It allows us to compare shapes and measures that aren’t the same size. The authors of this paper show that PGW is a reliable way to do this, and they even give us some new tools to help us solve problems using PGW. |
Keywords
* Artificial intelligence * Machine learning
