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An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists
Frédéric Chazal1, Bertrand Michel2
1Inria Saclay - Île-de-France Research Centre, Palaiseau, France.
Frontiers in Artificial Intelligence
|October 18, 2021
Summary
Topological data analysis (tda) offers new tools for understanding complex data structures. This introduction covers fundamental and practical aspects of tda for data analysis and statistical learning.
Area of Science:
- Data Science
- Computational Topology
- Statistical Learning
Background:
- Increasing data complexity necessitates advanced analytical methods.
- Traditional approaches struggle with high-dimensional and varied data.
Purpose of the Study:
- Introduce topological data analysis (tda) to non-experts.
- Highlight fundamental and practical applications of tda.
- Showcase tda's potential in data analysis and statistical learning.
Main Methods:
- Utilizes topological and geometric tools.
- Focuses on inferring structure from complex datasets.
- Presents selected topics for a foundational understanding.
Main Results:
- TDA provides novel methods for feature extraction.
- TDA tools can complement existing data analysis techniques.
- The field offers well-founded mathematical theories and computational tools.
Conclusions:
- TDA is a valuable emerging field for data analysis.
- Understanding tda principles enhances data interpretation capabilities.
- TDA offers a robust framework for exploring complex data structures.
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