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

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

ICML 2023poster1 citations

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

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

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.

BibTeX

@inproceedings{icml2023_towardsapersiste,
  title = {Towards a Persistence Diagram that is Robust to Noise and Varied Densities},
  author = {Hang Zhang and Kaifeng Zhang and Kai Ming Ting and Ye Zhu},
  booktitle = {ICML 2023},
  year = {2023}
}