Summary of Hierarchical Hybrid Sliced Wasserstein: a Scalable Metric For Heterogeneous Joint Distributions, by Khai Nguyen and Nhat Ho
Hierarchical Hybrid Sliced Wasserstein: A Scalable Metric for Heterogeneous Joint Distributions
by Khai Nguyen, Nhat Ho
First submitted to arxiv on: 23 Apr 2024
Categories
- Main: Computer Vision and Pattern Recognition (cs.CV)
- Secondary: Artificial Intelligence (cs.AI); Graphics (cs.GR); Machine Learning (cs.LG); 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 This paper proposes two new slicing operators, Partial Generalized Radon Transform (PGRT) and Hierarchical Hybrid Radon Transform (HHRT), to address the limitation of Sliced Wasserstein (SW) and Generalized Sliced Wasserstein (GSW) in comparing heterogeneous joint distributions. SW and GSW are widely used due to their computational and statistical scalability, but they are only defined between distributions supported on homogeneous domains. The proposed operators, PGRT and HHRT, aim to capture the structure of the joint supports set and enable meaningful comparisons. The authors extend SW into Hierarchical Hybrid Sliced Wasserstein (H2SW) distance, which is designed specifically for heterogeneous joint distributions. H2SW exhibits favorable performance in 3D mesh deformation, deep 3D mesh autoencoders, and datasets comparison. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper solves a big problem in comparing different types of data. Right now, we can only compare data that comes from the same kind of place (like all coming from the same city). But what if our data comes from different kinds of places? That’s where this new technique comes in. It helps us compare data even when it comes from different “places”. This is important because it means we can use this technique to compare things like 3D models, pictures, and more. The authors show that their new technique works really well in some tricky situations. |
