On some Properties of Expected Persistence Diagrams

Student: Kuznetsov Vitaliy

Educational Programme: Mathematics and Mathematical Physics (Master)

Year of Graduation: 2024

Topological Data Analysis (TDA) has emerged as a powerful tool for extracting meaningful features from complex data. However, its application to noisy data remains challenging due to its sensitivity to noise and outliers. In this paper, we propose a bootstrapping-based method that enhances the robustness of TDA. Our approach leverages the statistical properties of persistence diagrams to effectively filter out topological noise, ensuring accurate identification of significant features. We provide a background on TDA, describe our methodology, prove its correctness, and validate its efficacy through experiments on synthetic datasets. Our results demonstrate improvements in feature extraction from noisy data, paving the way for more robust applications of TDA in various fields.

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