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.
Previous Submission: No