Summary of Differentiable Mapper For Topological Optimization Of Data Representation, by Ziyad Oulhaj et al.
Differentiable Mapper For Topological Optimization Of Data Representation
by Ziyad Oulhaj, Mathieu Carrière, Bertrand Michel
First submitted to arxiv on: 20 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computational Geometry (cs.CG); Algebraic Topology (math.AT)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| 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 presents a breakthrough in Topological Data Analysis (TDA) and data science by developing an optimization framework to tune the filter parameter in Mapper graphs. The Mapper graph is a combinatorial graph that captures topological structures in data, but its utility has been limited due to manual parameter tuning. This work proposes a relaxed version of the Mapper graph and investigates its convergence properties. The authors demonstrate the effectiveness of their approach by optimizing Mapper graph representations on various datasets, showcasing improved results compared to arbitrary ones. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us better understand data by using special tools from topology. It’s like creating a map of your data, but instead of just showing where things are, it also shows how they’re connected. The problem is that this “map” needs some adjusting to get the most out of it. That’s what this research does – it figures out how to make those adjustments so we can get more insight from our data. |
Keywords
* Artificial intelligence * Optimization
