Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions
This work addresses the problem of classifying multidimensional persistence modules, which are underutilized in machine learning, for researchers working with topological data analysis.
This paper explores the use of lattice-based convolutional neural networks for classifying features derived from multiparameter persistence modules. The results indicate that this approach is a promising alternative for the classification of these complex data structures.
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.