A distribution-guided Mapper algorithm.

Area of Science:

• Topological Data Analysis
• Computational Biology
• Machine Learning

Background:

• The Mapper algorithm is crucial for visualizing complex dataset topology.
• Traditional Mapper methods use fixed parameters, potentially missing intricate data structures.
• Approximating Reeb graphs is a key application of Mapper.

Purpose of the Study:

• Introduce D-Mapper, a novel distribution-guided Mapper algorithm.
• Enhance topological feature extraction using probability models and intrinsic data properties.
• Develop a metric to evaluate Mapper-type algorithms based on clustering and persistent homology.

Main Methods:

• Developed D-Mapper algorithm utilizing probability models for density-guided covers.
• Introduced a new metric combining overlap clustering quality and extended persistent homology.
• Applied D-Mapper to SARS-COV-2 RNA sequence data.

Main Results:

• D-Mapper outperforms the classic Mapper algorithm across various scenarios.
• The algorithm effectively reveals subtle topological features.
• Analysis of SARS-COV-2 variants showed D-Mapper can uncover vertical and horizontal evolutionary patterns.

Conclusions:

• D-Mapper generates data covers guided by probability models.
• Fusing probabilistic models with Mapper algorithms offers powerful data exploration capabilities.