Summary of Computing Distances and Means on Manifolds with a Metric-constrained Eikonal Approach, by Daniel Kelshaw et al.
Computing distances and means on manifolds with a metric-constrained Eikonal approach
by Daniel Kelshaw, Luca Magri
First submitted to arxiv on: 12 Apr 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computational Geometry (cs.CG); Metric Geometry (math.MG)
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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 The paper introduces a novel solver called metric-constrained Eikonal, which generates continuous and differentiable representations of distance functions on Riemannian manifolds. This allows for the computation of globally length-minimizing paths on these complex structures. The authors demonstrate the applicability of this approach to various manifolds, including Gaussian mixture models and clustering tasks, outperforming existing methods in terms of computational efficiency. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper makes it possible to calculate distances on complex shapes like Riemannian manifolds, which has many uses in science. The new method, called metric-constrained Eikonal, gives us a way to find the shortest paths on these shapes and even group similar points together without needing lots of computation power. |
Keywords
* Artificial intelligence * Clustering
