Summary of A Mapper Algorithm with Implicit Intervals and Its Optimization, by Yuyang Tao and Shufei Ge
A Mapper Algorithm with implicit intervals and its optimization
by Yuyang Tao, Shufei Ge
First submitted to arxiv on: 16 Dec 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 The Mapper algorithm is a crucial tool for visualizing complex data in topology data analysis and biomedical research. It generates a combinatorial graph that implies the shape of the data, but its performance can be impeded by manual parameter tuning and fixed intervals. To address these limitations, we introduce a novel framework that implicitly represents intervals through a hidden assignment matrix, enabling automatic parameter optimization via stochastic gradient descent. Our soft Mapper framework uses a Gaussian mixture model for flexible interval construction and a topological loss function for optimizing parameters. Simulation and application studies demonstrate its effectiveness in capturing underlying topological structures. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The Mapper algorithm helps scientists understand complex data by turning it into a graph that shows its shape. But, this process can be tricky because you need to set the right parameters and intervals just right. To make it easier, we created a new way of doing things that uses a special kind of math called stochastic gradient descent. Our new approach lets computers automatically find the best settings for the algorithm without needing human help. We tested our method on real data from people with Alzheimer’s disease and found that it works well. |
Keywords
» Artificial intelligence » Loss function » Mixture model » Optimization » Stochastic gradient descent
