Generalized Laplacian Regularized Framelet Graph Neural Networks

Graph neural networks (GNNs) have demonstrated remarkable ability for graph learning tasks (Bronstein et al, 2017; Wu et al, 2020; Zhang et al, 2022; Zhou et al, 2020). The input to GNNs is the so-called graph data which records useful features and structural information among data. Such data are widely seen in many fields, such as biomedical science (Ahmedt-Aristizabal et al, 2021), social networks (Fan et al, 2019), and recommend systems (Wu et al, 2022). GNN models can be broadly categorized into spectral and spatial methods. The spatial methods such as MPNN (Gilmer et al, 2017), GAT (Veličković et al, 2018) and GIN (Xu et al, 2018a) utilize the message passing mechanism to propagate node feature information based on their neighbours (Scarselli et al, 2009). On the other hand, the spectral methods including ChebyNet (Defferrard et al, 2016), GCN (Kipf and Welling, 2017) and BernNet (He et al, 2021) are derived from the classic convolutional networks, treating the input graph data as signals (i.e., a function with the domain of graph nodes) (Ortega et al, 2018), and filtering signals in the Fourier domain (Bruna et al, 2014; Defferrard et al, 2016).