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The aim is to provide insights into the foundations, algorithms, and applications of topological data analysis (TDA) in complex data settings.

June 20, 2026MathematicsOpen Access

Topological Data Analysis: Foundations, Algorithms, and Emerging Applications

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The aim is to provide insights into the foundations, algorithms, and applications of topological data analysis (TDA) in complex data settings.
Survey of recent developments in TDA, emphasizing articles from 2024-2025.
Presentation of mathematical and computational foundations including persistent homology and the Mapper algorithm.
Review of applications across diverse fields such as biomedical research, finance, and engineering.
TDA effectively extracts features from high-dimensional data, aiding in understanding complex systems.
Identified recurrent failure patterns indicate that TDA performance can be sensitive to methodological choices.
Challenges in scalability, statistical foundations, and integration with AI highlight the need for future research.

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Survey summarizes advancements in topological data analysis in various fields, highlighting challenges and future directions.

Georgiou et al. (2026) studied this question.

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