ATOL: Measure Vectorization for Automatic Topologically-Oriented Learning

Martin Royer, Frederic Chazal, Clément Levrard, Yuhei Umeda, Yuichi Ike
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1000-1008, 2021.

Abstract

Robust topological information commonly comes in the form of a set of persistence diagrams, finite measures that are in nature uneasy to affix to generic machine learning frameworks. We introduce a fast, learnt, unsupervised vectorization method for measures in Euclidean spaces and use it for reflecting underlying changes in topological behaviour in machine learning contexts. The algorithm is simple and efficiently discriminates important space regions where meaningful differences to the mean measure arise. It is proven to be able to separate clusters of persistence diagrams. We showcase the strength and robustness of our approach on a number of applications, from emulous and modern graph collections where the method reaches state-of-the-art performance to a geometric synthetic dynamical orbits problem. The proposed methodology comes with a single high level tuning parameter: the total measure encoding budget. We provide a completely open access software.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-royer21a, title = { ATOL: Measure Vectorization for Automatic Topologically-Oriented Learning }, author = {Royer, Martin and Chazal, Frederic and Levrard, Cl{\'e}ment and Umeda, Yuhei and Ike, Yuichi}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {1000--1008}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/royer21a/royer21a.pdf}, url = {https://proceedings.mlr.press/v130/royer21a.html}, abstract = { Robust topological information commonly comes in the form of a set of persistence diagrams, finite measures that are in nature uneasy to affix to generic machine learning frameworks. We introduce a fast, learnt, unsupervised vectorization method for measures in Euclidean spaces and use it for reflecting underlying changes in topological behaviour in machine learning contexts. The algorithm is simple and efficiently discriminates important space regions where meaningful differences to the mean measure arise. It is proven to be able to separate clusters of persistence diagrams. We showcase the strength and robustness of our approach on a number of applications, from emulous and modern graph collections where the method reaches state-of-the-art performance to a geometric synthetic dynamical orbits problem. The proposed methodology comes with a single high level tuning parameter: the total measure encoding budget. We provide a completely open access software. } }
Endnote
%0 Conference Paper %T ATOL: Measure Vectorization for Automatic Topologically-Oriented Learning %A Martin Royer %A Frederic Chazal %A Clément Levrard %A Yuhei Umeda %A Yuichi Ike %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-royer21a %I PMLR %P 1000--1008 %U https://proceedings.mlr.press/v130/royer21a.html %V 130 %X Robust topological information commonly comes in the form of a set of persistence diagrams, finite measures that are in nature uneasy to affix to generic machine learning frameworks. We introduce a fast, learnt, unsupervised vectorization method for measures in Euclidean spaces and use it for reflecting underlying changes in topological behaviour in machine learning contexts. The algorithm is simple and efficiently discriminates important space regions where meaningful differences to the mean measure arise. It is proven to be able to separate clusters of persistence diagrams. We showcase the strength and robustness of our approach on a number of applications, from emulous and modern graph collections where the method reaches state-of-the-art performance to a geometric synthetic dynamical orbits problem. The proposed methodology comes with a single high level tuning parameter: the total measure encoding budget. We provide a completely open access software.
APA
Royer, M., Chazal, F., Levrard, C., Umeda, Y. & Ike, Y.. (2021). ATOL: Measure Vectorization for Automatic Topologically-Oriented Learning . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1000-1008 Available from https://proceedings.mlr.press/v130/royer21a.html.

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