A Comparative Study of Machine Learning Methods for Persistence Diagrams.

Area of Science:

• Topological Data Analysis
• Machine Learning
• Computational Geometry

Background:

• Featurization maps persistence diagrams to Euclidean space, preserving structural information.
• Numerous featurization methods exist, but systematic comparisons and standardized datasets are lacking.

Purpose of the Study:

• To conduct a methodical comparison of prominent featurization techniques for persistence diagrams.
• To evaluate the predictive utility of these methods on diverse, real-world datasets.

Main Methods:

• Review and evaluation of stable multi-scale kernel, persistence landscapes, persistence images, ring of algebraic functions, template functions, and adaptive template systems.
• Application of machine learning algorithms using features extracted by these methods.
• Testing on benchmark datasets: MNIST, SHREC14, Protein, MPEG7, and HAM10000.

Main Results:

• Comparative analysis of featurization method performance across different data types.
• Assessment of the impact of featurization choices on machine learning model accuracy.
• Identification of strengths and weaknesses of each featurization approach.

Conclusions:

• Provides a benchmark for selecting appropriate featurization methods in topological data analysis.
• Highlights the importance of featurization choice for downstream machine learning tasks.
• Offers guidance for researchers and practitioners in applying topological features to real-world problems.