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This study aims to compare persistent homology and the Mapper algorithm in extracting structural information from high-dimensional datasets.

A Comparative Study of Persistence and Mapper in Topological Data Analysis

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This study aims to compare persistent homology and the Mapper algorithm in extracting structural information from high-dimensional datasets.
Applied persistent homology and Mapper to the Wisconsin Breast Cancer Dataset
Analyzed the structural information provided by each method
Utilized Wasserstein distances to support visual persistent homology analysis
Persistent homology identified distinct topological structures between benign and malignant groups (1-Wasserstein distance)
Mapper highlighted clustering and local connectivity in feature space
Combined analysis revealed transition zones and class-dominated subgraphs

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Comparative analysis reveals complementary insights of persistent homology and mapper in cancer datasets, suggesting enhanced data understanding.

Marline et al. (2026) studied this question.

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Comparative analysis reveals complementary insights of persistent homology and mapper in cancer datasets, suggesting enhanced data understanding.