Graph Filtration Learning

Christoph Hofer, Florian Graf, Bastian Rieck, Marc Niethammer, Roland Kwitt
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:4314-4323, 2020.

Abstract

We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this end, we leverage persistent homology computed via a real-valued, learnable, filter function. We establish the theoretical foundation for differentiating through the persistent homology computation. Empirically, we show that this type of readout operation compares favorably to previous techniques, especially when the graph connectivity structure is informative for the learning problem.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-hofer20b, title = {Graph Filtration Learning}, author = {Hofer, Christoph and Graf, Florian and Rieck, Bastian and Niethammer, Marc and Kwitt, Roland}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {4314--4323}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/hofer20b/hofer20b.pdf}, url = {https://proceedings.mlr.press/v119/hofer20b.html}, abstract = {We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this end, we leverage persistent homology computed via a real-valued, learnable, filter function. We establish the theoretical foundation for differentiating through the persistent homology computation. Empirically, we show that this type of readout operation compares favorably to previous techniques, especially when the graph connectivity structure is informative for the learning problem.} }
Endnote
%0 Conference Paper %T Graph Filtration Learning %A Christoph Hofer %A Florian Graf %A Bastian Rieck %A Marc Niethammer %A Roland Kwitt %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-hofer20b %I PMLR %P 4314--4323 %U https://proceedings.mlr.press/v119/hofer20b.html %V 119 %X We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this end, we leverage persistent homology computed via a real-valued, learnable, filter function. We establish the theoretical foundation for differentiating through the persistent homology computation. Empirically, we show that this type of readout operation compares favorably to previous techniques, especially when the graph connectivity structure is informative for the learning problem.
APA
Hofer, C., Graf, F., Rieck, B., Niethammer, M. & Kwitt, R.. (2020). Graph Filtration Learning. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:4314-4323 Available from https://proceedings.mlr.press/v119/hofer20b.html.

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