Persistence weighted Gaussian kernel for topological data analysis

Genki Kusano, Yasuaki Hiraoka, Kenji Fukumizu
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:2004-2013, 2016.

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 this Paper

BibTeX
@InProceedings{pmlr-v48-kusano16, title = {Persistence weighted Gaussian kernel for topological data analysis}, author = {Kusano, Genki and Hiraoka, Yasuaki and Fukumizu, Kenji}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {2004--2013}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/kusano16.pdf}, url = {https://proceedings.mlr.press/v48/kusano16.html}, 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.} }
Endnote
%0 Conference Paper %T Persistence weighted Gaussian kernel for topological data analysis %A Genki Kusano %A Yasuaki Hiraoka %A Kenji Fukumizu %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-kusano16 %I PMLR %P 2004--2013 %U https://proceedings.mlr.press/v48/kusano16.html %V 48 %X 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.
RIS
TY - CPAPER TI - Persistence weighted Gaussian kernel for topological data analysis AU - Genki Kusano AU - Yasuaki Hiraoka AU - Kenji Fukumizu BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-kusano16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 2004 EP - 2013 L1 - http://proceedings.mlr.press/v48/kusano16.pdf UR - https://proceedings.mlr.press/v48/kusano16.html AB - 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. ER -
APA
Kusano, G., Hiraoka, Y. & Fukumizu, K.. (2016). Persistence weighted Gaussian kernel for topological data analysis. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:2004-2013 Available from https://proceedings.mlr.press/v48/kusano16.html.

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