Dist2Cycle: A Simplicial Neural Network for Homology Localization
Keywords:Machine Learning (ML), Knowledge Representation And Reasoning (KRR)
AbstractSimplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher dimensional topological features of data, features to which graphs, encoding only pairwise relationships, remain oblivious. While attempts have been made to extend Graph Neural Networks (GNNs) to a simplicial complex setting, the methods do not inherently exploit, or reason about, the underlying topological structure of the network. We propose a graph convolutional model for learning functions parametrized by the k-homological features of simplicial complexes. By spectrally manipulating their combinatorial k-dimensional Hodge Laplacians, the proposed model enables learning topological features of the underlying simplicial complexes, specifically, the distance of each k-simplex from the nearest "optimal" k-th homology generator, effectively providing an alternative to homology localization.
How to Cite
Keros, A. D., Nanda, V., & Subr, K. (2022). Dist2Cycle: A Simplicial Neural Network for Homology Localization. Proceedings of the AAAI Conference on Artificial Intelligence, 36(7), 7133-7142. https://doi.org/10.1609/aaai.v36i7.20673
AAAI Technical Track on Machine Learning II