Graph Learning in 4D: a Quaternion-valued Laplacian to Enhance Spectral GCNs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911743241879552 |
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| author | Fiorini, Stefano Coniglio, Stefano Ciavotta, Michele Messina, Enza |
| author_facet | Fiorini, Stefano Coniglio, Stefano Ciavotta, Michele Messina, Enza |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17361 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Graph Learning in 4D: a Quaternion-valued Laplacian to Enhance Spectral GCNs Fiorini, Stefano Coniglio, Stefano Ciavotta, Michele Messina, Enza Machine Learning 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. |
| title | Graph Learning in 4D: a Quaternion-valued Laplacian to Enhance Spectral GCNs |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2312.17361 |