We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Generalized Persistence for Equivariant Operators in Machine Learning.
- Authors
Bergomi, Mattia G.; Ferri, Massimo; Mella, Alessandro; Vertechi, Pietro
- Abstract
Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines fully aware of data constraints and symmetries. We introduce an original class of neural network layers based on a generalization of topological persistence. The proposed persistence-based layers allow the users to encode specific data properties (e.g., equivariance) easily. Additionally, these layers can be trained through standard optimization procedures (backpropagation) and composed with classical layers. We test the performance of generalized persistence-based layers as pooling operators in convolutional neural networks for image classification on the MNIST, Fashion-MNIST and CIFAR-10 datasets.
- Subjects
ARTIFICIAL neural networks; DATA analysis; MACHINE learning; ARTIFICIAL intelligence; TOPOLOGICAL derivatives
- Publication
Machine Learning & Knowledge Extraction, 2023, Vol 5, Issue 2, p346
- ISSN
2504-4990
- Publication type
Article
- DOI
10.3390/make5020021