拉普拉斯矩阵
拉普拉斯算子
符号(数学)
计算机科学
图形
数学
离散数学
组合数学
理论计算机科学
算法
数学分析
作者
Stefano Fiorini,Stefano Coniglio,Michele Ciavotta,Enza Messina
出处
期刊:Proceedings of the ... AAAI Conference on Artificial Intelligence
[Association for the Advancement of Artificial Intelligence (AAAI)]
日期:2023-06-26
卷期号:37 (6): 7568-7576
被引量:1
标识
DOI:10.1609/aaai.v37i6.25919
摘要
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 (LSM), a new Laplacian matrix that we introduce ex novo in this work. LSM 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. LSM 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. LSM 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.
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