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Graph Learning in 4D: A Quaternion-Valued Laplacian to Enhance Spectral GCNs
Graph Learning in 4D: A Quaternion-Valued Laplacian to Enhance Spectral GCNs
- Publication Year :
- 2024
-
Abstract
- We introduce QuaterGCN, a spectral Graph Convolutional Network (GCN) with quaternion-valued weights at whose core lies the Quaternionic Laplacian, a quaternion-valued Laplacian matrix by whose proposal we generalize two widely-used Laplacian matrices: the classical Laplacian (defined for undirected graphs) and the complex-valued Sign-Magnetic Laplacian (proposed to handle digraphs with weights of arbitrary sign). In addition to its generality, our Quaternionic Laplacian is the only Laplacian to completely preserve the topology of a digraph, as it can handle graphs and digraphs containing antiparallel pairs of edges (digons) of different weights without reducing them to a single (directed or undirected) edge as done with other Laplacians. Experimental results show the superior performance of QuaterGCN compared to other state-of-the-art GCNs, particularly in scenarios where the information the digons carry is crucial to successfully address the task at hand.
Details
- Database :
- OAIster
- Notes :
- English
- Publication Type :
- Electronic Resource
- Accession number :
- edsoai.on1440494002
- Document Type :
- Electronic Resource