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

Hang Zhang, Kaifeng Zhang, Kai Ming Ting, Ye Zhu
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:41952-41972, 2023.

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 this Paper

BibTeX
@InProceedings{pmlr-v202-zhang23bb, 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 = {Proceedings of the 40th International Conference on Machine Learning}, pages = {41952--41972}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/zhang23bb/zhang23bb.pdf}, url = {https://proceedings.mlr.press/v202/zhang23bb.html}, 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.} }
Endnote
%0 Conference Paper %T Towards a Persistence Diagram that is Robust to Noise and Varied Densities %A Hang Zhang %A Kaifeng Zhang %A Kai Ming Ting %A Ye Zhu %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-zhang23bb %I PMLR %P 41952--41972 %U https://proceedings.mlr.press/v202/zhang23bb.html %V 202 %X 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.
APA
Zhang, H., Zhang, K., Ting, K.M. & Zhu, Y.. (2023). Towards a Persistence Diagram that is Robust to Noise and Varied Densities. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:41952-41972 Available from https://proceedings.mlr.press/v202/zhang23bb.html.

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