Minimum Spanning vs. Principal Trees for Structured Approximations of Multi-Dimensional Datasets.

Area of Science:

• Computational Biology
• Data Science
• Graph Theory

Background:

• Graph-based approximations are vital for analyzing complex, multi-dimensional data, including single-cell trajectory inference and image skeletonization.
• Existing methods for constructing these graphs, such as minimum spanning trees and principal graphs, lack standardized benchmarking and hyperparameter definition.
• Direct graph comparison is challenging due to variations in topology and complexity.

Purpose of the Study:

• To propose and validate a novel methodology for comparing and benchmarking graph-based data approximation methods.
• To establish a framework for defining hyperparameters for graph construction algorithms.
• To enable efficient comparison of arbitrary graph topologies and complexities.

Main Methods:

• A new benchmarking methodology is introduced, avoiding direct graph comparison.
• The approach induces data point cloud clustering from graph approximations.
• Clustering is achieved by decomposing graphs into segments and assigning data points to the nearest segment, with mutual information used for scoring.

Main Results:

• The proposed methodology effectively compares diverse graph-based data approximation techniques.
• Mutual information-based scoring proves useful for evaluating data partitioning induced by graphs.
• The method is implemented in Python utilizing scikit-learn for high performance.

Conclusions:

• The developed methodology provides a robust framework for benchmarking graph-based data approximations.
• This approach facilitates objective comparison and hyperparameter tuning for methods used in single-cell data analysis and beyond.
• The Python implementation ensures efficiency and broad applicability.