Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions
arXiv:2011.14057
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.
References in corpus (7)
- A roadmap for the computation of persistent homology
- Statistical topological data analysis using persistence landscapes
- Interactive Visualization of 2-D Persistence Modules
- A Topology Layer for Machine Learning
- Edit Distance and Persistence Diagrams Over Lattices
- Powerset Convolutional Neural Networks
- Invertibility in Category Representations