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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

Authors :
Wooldridge, M
Dy, J
Natarajan, S
Fiorini, S
Coniglio, S
Ciavotta, M
Messina, E
Fiorini S.
Coniglio S.
Ciavotta M.
Messina E.
Wooldridge, M
Dy, J
Natarajan, S
Fiorini, S
Coniglio, S
Ciavotta, M
Messina, E
Fiorini S.
Coniglio S.
Ciavotta M.
Messina E.
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