Multidimensional Persistence Module Classification via Lattice-Theoretic ConvolutionsDownload PDF

10 Oct 2020, 16:50 (modified: 29 Jul 2022, 18:55)TDA & Beyond 2020 SpotlightReaders: Everyone
Keywords: persistent homology, multidimensional persistence, neural networks, lattice theory, signal processing
TL;DR: Lattice-based convolutional networks beat classical convolutional networks in classifying (certain) 2d persistence modules.
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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