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arXiv · 2312.17361

Graph Learning in 4D: a Quaternion-valued Laplacian to Enhance Spectral GCNs

Stefano Fiorini·Stefano Coniglio·Michele Ciavotta·Enza Messina
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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.

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Stefano Fiorini, Stefano Coniglio, Michele Ciavotta, Enza Messina. 2023-12-28. Graph Learning in 4D: a Quaternion-valued Laplacian to Enhance Spectral GCNs. https://arxiv.org/abs/2312.17361

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