This paper introduces SigMaNet, a generalized Graph Convolutional Network (GCN) capable of handling both undirected and directed graphs with weights not restricted in sign nor magnitude. The cornerstone of SigMaNet is the Sign-Magnetic Laplacian (Lσ), a new Laplacian matrix that we introduce ex novo in this work. Lσ allows us to bridge a gap in the current literature by extending the theory of spectral GCNs to (directed) graphs with both positive and negative weights. Lσ exhibits several desirable properties not enjoyed by other Laplacian matrices on which several state-of-the-art architectures are based, among which encoding the edge direction and weight in a clear and natural way that is not negatively affected by the weight magnitude. Lσ is also completely parameter-free, which is not the case of other Laplacian operators such as, e.g., the Magnetic Laplacian. The versatility and the performance of our proposed approach is amply demonstrated via computational experiments. Indeed, our results show that, for at least a metric, SigMaNet achieves the best performance in 15 out of 21 cases and either the first- or second-best performance in 21 cases out of 21, even when compared to architectures that are either more complex or that, due to being designed for a narrower class of graphs, should—but do not—achieve a better performance.

Fiorini, S., Coniglio, S., Ciavotta, M., Messina, E. (2023). SigMaNet: One Laplacian to Rule Them All. In Proceedings of the 37th AAAI Conference on Artificial Intelligence, AAAI 2023 (pp.7568-7576). AAAI Press [10.1609/aaai.v37i6.25919].

SigMaNet: One Laplacian to Rule Them All

Fiorini, Stefano
;
Ciavotta, Michele;Messina, Enza
2023

Abstract

This paper introduces SigMaNet, a generalized Graph Convolutional Network (GCN) capable of handling both undirected and directed graphs with weights not restricted in sign nor magnitude. The cornerstone of SigMaNet is the Sign-Magnetic Laplacian (Lσ), a new Laplacian matrix that we introduce ex novo in this work. Lσ allows us to bridge a gap in the current literature by extending the theory of spectral GCNs to (directed) graphs with both positive and negative weights. Lσ exhibits several desirable properties not enjoyed by other Laplacian matrices on which several state-of-the-art architectures are based, among which encoding the edge direction and weight in a clear and natural way that is not negatively affected by the weight magnitude. Lσ is also completely parameter-free, which is not the case of other Laplacian operators such as, e.g., the Magnetic Laplacian. The versatility and the performance of our proposed approach is amply demonstrated via computational experiments. Indeed, our results show that, for at least a metric, SigMaNet achieves the best performance in 15 out of 21 cases and either the first- or second-best performance in 21 cases out of 21, even when compared to architectures that are either more complex or that, due to being designed for a narrower class of graphs, should—but do not—achieve a better performance.
paper
ML: Graph-based Machine Learning, ML: Deep Neural Architectures, ML: Matrix & Tensor Methods
English
37th AAAI Conference on Artificial Intelligence, AAAI 2023 - 7 February 2023 through 14 February 2023
2023
Williams, B; Chen, Y; Neville, J
Proceedings of the 37th AAAI Conference on Artificial Intelligence, AAAI 2023
9781577358800
2023
37
6
7568
7576
open
Fiorini, S., Coniglio, S., Ciavotta, M., Messina, E. (2023). SigMaNet: One Laplacian to Rule Them All. In Proceedings of the 37th AAAI Conference on Artificial Intelligence, AAAI 2023 (pp.7568-7576). AAAI Press [10.1609/aaai.v37i6.25919].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/454040
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