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.
Cite
Text
Zhang et al. "Towards a Persistence Diagram That Is Robust to Noise and Varied Densities." International Conference on Machine Learning, 2023.Markdown
[Zhang et al. "Towards a Persistence Diagram That Is Robust to Noise and Varied Densities." International Conference on Machine Learning, 2023.](https://mlanthology.org/icml/2023/zhang2023icml-persistence/)BibTeX
@inproceedings{zhang2023icml-persistence,
title = {{Towards a Persistence Diagram That Is Robust to Noise and Varied Densities}},
author = {Zhang, Hang and Zhang, Kaifeng and Ting, Kai Ming and Zhu, Ye},
booktitle = {International Conference on Machine Learning},
year = {2023},
pages = {41952-41972},
volume = {202},
url = {https://mlanthology.org/icml/2023/zhang2023icml-persistence/}
}