Persistence Weighted Gaussian Kernel for Topological Data Analysis
Abstract
Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy topological properties. This paper proposes a kernel method on persistence diagrams to develop a statistical framework in TDA. The proposed kernel satisfies the stability property and provides explicit control on the effect of persistence. Furthermore, the method allows a fast approximation technique. The method is applied into practical data on proteins and oxide glasses, and the results show the advantage of our method compared to other relevant methods on persistence diagrams.
Cite
Text
Kusano et al. "Persistence Weighted Gaussian Kernel for Topological Data Analysis." International Conference on Machine Learning, 2016.Markdown
[Kusano et al. "Persistence Weighted Gaussian Kernel for Topological Data Analysis." International Conference on Machine Learning, 2016.](https://mlanthology.org/icml/2016/kusano2016icml-persistence/)BibTeX
@inproceedings{kusano2016icml-persistence,
title = {{Persistence Weighted Gaussian Kernel for Topological Data Analysis}},
author = {Kusano, Genki and Hiraoka, Yasuaki and Fukumizu, Kenji},
booktitle = {International Conference on Machine Learning},
year = {2016},
pages = {2004-2013},
volume = {48},
url = {https://mlanthology.org/icml/2016/kusano2016icml-persistence/}
}