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2023 ICML ICML 2023

Towards a Persistence Diagram that is Robust to Noise and Varied Densities

Abstract

Recent works have identified that existing methods, which construct persistence diagrams in Topological Data Analysis (TDA), are not robust to noise and varied densities in a point cloud. We analyze the necessary properties of an approach that can address these two issues, and propose a new filter function for TDA based on a new data-dependent kernel which possesses these properties. Our empirical evaluation reveals that the proposed filter function provides a better means for t-SNE visualization and SVM classification than three existing methods of TDA.

🧭 Keyword Pioneer — data-dependent kernel
🐝 Cross-Pollinator — Artificial Intelligence, Computer Vision, Data Science & Analytics, Deep Learning, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning, Robotics, Speech & Audio
🌉 Interdisciplinary Bridge — Data Science & Analytics and Machine Learning

Authors

Hang Zhang , Kaifeng Zhang , Kai Ming Ting , Ye Zhu

Topics

Machine Learning > Core Methods > Representation Learning Data Science & Analytics > Methods > Data Mining Machine Learning > Core Methods > Dimensionality Reduction Machine Learning > Core Methods > Kernel Methods

Keywords

point cloud topological data analysis noise robustness support vector machine persistence diagram data-dependent kernel filter function kernel methods t-sne visualization
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