Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions

Abstract

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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Cite

Text

Riess and Hansen. "Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions." NeurIPS 2020 Workshops: TDA_and_Beyond, 2020.

Markdown

[Riess and Hansen. "Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions." NeurIPS 2020 Workshops: TDA_and_Beyond, 2020.](https://mlanthology.org/neuripsw/2020/riess2020neuripsw-multidimensional/)

BibTeX

@inproceedings{riess2020neuripsw-multidimensional,
  title     = {{Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions}},
  author    = {Riess, Hans Matthew and Hansen, Jakob},
  booktitle = {NeurIPS 2020 Workshops: TDA_and_Beyond},
  year      = {2020},
  url       = {https://mlanthology.org/neuripsw/2020/riess2020neuripsw-multidimensional/}
}