Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions

Hans Matthew Riess, Jakob Hansen

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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