A Topology Layer for Machine Learning
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Publication:6319554
arXiv1905.12200MaRDI QIDQ6319554
Leonidas J. Guibas, Anjan Dwaraknath, Bradley J. Nelson, Rickard Brüel-Gabrielsson, Primoz Skraba, Gunnar Carlsson
Publication date: 28 May 2019
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 edge-based filtrations. We present three novel applications: the topological layer can (i) regularize data reconstruction 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 (www.github.com/bruel-gabrielsson/TopologyLayer) is publicly available and we hope its availability will facilitate the use of persistent homology in deep learning and other gradient based applications.
Has companion code repository: https://github.com/bruel-gabrielsson/TopologyLayer
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