Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions

Published in NeurIPS Workshop: Topological Data Analysis and Beyond, 2020

Recommended citation: Riess, H., & Hansen, J. (2020). Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions. arXiv preprint. https://arxiv.org/pdf/2011.14057.pdf

Multiparameter persistent homology has been largely neglected as an input to machine learning algorithms. We consider the use of lattice-based convolutional neural network layers as a tool for the analysis of features arising from multiparameter persistence modules. We find that these show promise as an alternative to convolutions for the classification of multidimensional persistence modules.

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