Summary of Improving Mapper’s Robustness by Varying Resolution According to Lens-space Density, By Kaleb D. Ruscitti and Leland Mcinnes
Improving Mapper’s Robustness by Varying Resolution According to Lens-Space Density
by Kaleb D. Ruscitti, Leland McInnes
First submitted to arxiv on: 4 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Algebraic Topology (math.AT); 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 improvements to the Mapper algorithm by removing assumptions about a single resolution scale across semantic space and enhancing robustness under parameter changes. The modification incorporates local density into the choice of cover for Mapper, making it more suitable for datasets with variable local density in the Morse function used for Mapper. Additionally, the authors prove that the modified Mapper still converges to the Reeb graph of the Rips complex, but captures more topological features than traditional Mapper. Computational experiments and implementation details are also discussed. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper makes a computer algorithm better by removing some rules it had to follow. It helps the algorithm be more reliable when given different settings. The change lets the algorithm work better on datasets that have varying levels of detail in certain areas. The authors also prove that their modified algorithm still produces accurate results, but with more useful information. They share examples and explain how they implemented these changes. |
