A Topology Layer for Machine Learning. Brüel-Gabrielsson, R.; Nelson, B. J.; Dwaraknath, A.; Skraba, P.; Guibas, L. J.; and Carlsson, G.
A Topology Layer for Machine Learning [link]Paper  abstract   bibtex   
Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set filtrations and distance-bases filtrations. We present three novel applications: the topological layer can (i) serve as a regularizer directly on data or the weights of machine learning models, (ii) construct a loss on the output of a deep generative network to incorporate topological priors, and (iii) perform topological adversarial attacks on deep networks trained with persistence features. The code is publicly available and we hope its availability will facilitate the use of persistent homology in deep learning and other gradient based applications.
@article{bruel-gabrielssonTopologyLayerMachine2019,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1905.12200},
  primaryClass = {cs, stat},
  title = {A {{Topology Layer}} for {{Machine Learning}}},
  url = {http://arxiv.org/abs/1905.12200},
  abstract = {Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set filtrations and distance-bases filtrations. We present three novel applications: the topological layer can (i) serve as a regularizer directly on data or the weights of machine learning models, (ii) construct a loss on the output of a deep generative network to incorporate topological priors, and (iii) perform topological adversarial attacks on deep networks trained with persistence features. The code is publicly available and we hope its availability will facilitate the use of persistent homology in deep learning and other gradient based applications.},
  urldate = {2019-06-03},
  date = {2019-05-28},
  keywords = {Statistics - Machine Learning,Computer Science - Machine Learning},
  author = {Brüel-Gabrielsson, Rickard and Nelson, Bradley J. and Dwaraknath, Anjan and Skraba, Primoz and Guibas, Leonidas J. and Carlsson, Gunnar},
  file = {/home/dimitri/Nextcloud/Zotero/storage/M2QTLMQG/Brüel-Gabrielsson et al. - 2019 - A Topology Layer for Machine Learning.pdf;/home/dimitri/Nextcloud/Zotero/storage/S6DIBJTQ/1905.html}
}
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