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1. Mapping Brain Structural Connectivities to Functional Networks Via Graph Encoder-Decoder With Interpretable Latent Embeddings

   https://doi.org/10.1109/GlobalSIP45357.2019.8969239  

   Li, Yang ; Shafipour, Rasoul ; Mateos, Gonzalo ; Zhang, Zhengwu ( November 2019 , 2019 IEEE Global Conference on Signal and Information Processing (GlobalSIP))

   In this paper, the relationship between functional and structural brain networks is investigated by training a graph encoder-decoder system to learn the mapping from brain structural connectivity (SC) to functional connectivity (FC). Our work leverages a graph convolutional network (GCN) model in the encoder which integrates both nodal attributes and the network topology information to generate new graph representations in lower dimensions. Using brain SC graphs as inputs, the novel GCN-based encoder-decoder system manages to account for both direct and indirect interactions between brain regions to reconstruct the empirical FC networks. In doing so, the latent variables within the system (i.e., the learnt low-dimensional embeddings) capture important information regarding the relation between functional and structural networks. By decomposing the reconstructed functional networks in terms of the output of each graph convolution filter, we can extract those brain regions which contribute most to the generation of FC networks from their SC counterparts. Experiments on a large population of healthy subjects from the Human Connectome Project show our model can learn a generalizable and interpretable SC-FC relationship. Overall, results here support the promising prospect of using GCNs to discover more about the complex nature of human brain activity and function.
2. WMGCN: Weighted Meta-Graph Based Graph Convolutional Networks for Representation Learning in Heterogeneous Networks

   JINLI ZHANG, ZONGLI JIANG ( April 2020 , IEEE access)

   Network embedding has been an effective tool to analyze heterogeneous networks (HNs) by representing nodes in a low-dimensional space. Although many recent methods have been proposed for representation learning of HNs, there is still much room for improvement. Random walks based methods are currently popular methods to learn network embedding; however, they are random and limited by the length of sampled walks, and have difculty capturing network structural information. Some recent researches proposed using meta paths to express the sample relationship in HNs. Another popular graph learning model, the graph convolutional network (GCN) is known to be capable of better exploitation of network topology, but the current design of GCN is intended for homogenous networks. This paper proposes a novel combination of meta-graph and graph convolution, the meta-graph based graph convolutional networks (MGCN). To fully capture the complex long semantic information, MGCN utilizes different meta-graphs in HNs. As different meta-graphs express different semantic relationships, MGCN learns the weights of different meta-graphs to make up for the loss of semantics when applying GCN. In addition, we improve the current convolution design by adding node self-signicance. To validate our model in learning feature representation, we present comprehensive experiments on four real-world datasetsmore »and two representation tasks: classication and link prediction. WMGCN's representations can improve accuracy scores by up to around 10% in comparison to other popular representation learning models. What's more, WMGCN'feature learning outperforms other popular baselines. The experimental results clearly show our model is superior over other state-of-the-art representation learning algorithms.« less
3. Geometric Graph Representation Learning via Maximizing Rate Reduction

   https://doi.org/10.1145/3485447.3512170  

   Han, Xiaotian ; Jiang, Zhimeng ; Liu, Ninghao ; Song, Qingquan ; Li, Jundong ; Hu, Xia ( April 2022 , Proceedings of the ACM Web Conference 2022)

   Learning discriminative node representations benefits various downstream tasks in graph analysis such as community detection and node classification. Existing graph representation learning methods (e.g., based on random walk and contrastive learning) are limited to maximizing the local similarity of connected nodes. Such pair-wise learning schemes could fail to capture the global distribution of representations, since it has no explicit constraints on the global geometric properties of representation space. To this end, we propose Geometric Graph Representation Learning (G2R) to learn node representations in an unsupervised manner via maximizing rate reduction. In this way, G2R maps nodes in distinct groups (implicitly stored in the adjacency matrix) into different subspaces, while each subspace is compact and different subspaces are dispersedly distributed. G2R adopts a graph neural network as the encoder and maximizes the rate reduction with the adjacency matrix. Furthermore, we theoretically and empirically demonstrate that rate reduction maximization is equivalent to maximizing the principal angles between different subspaces. Experiments on real-world datasets show that G2R outperforms various baselines on node classification and community detection tasks.
4. Hyperbolic Graph Convolutional Neural Networks

   Chami, I. ; Ying, R. ; Ré, C. ; Leskovec, J. ( December 2019 , Advances in neural information processing systems)

   Graph convolutional neural networks (GCNs) embed nodes in a graph into Euclidean space, which has been shown to incur a large distortion when embedding real-world graphs with scale-free or hierarchical structure. Hyperbolic geometry offers an exciting alternative, as it enables embeddings with much smaller distortion. However, extending GCNs to hyperbolic geometry presents several unique challenges because it is not clear how to define neural network operations, such as feature transformation and aggregation, in hyperbolic space. Furthermore, since input features are often Euclidean, it is unclear how to transform the features into hyperbolic embeddings with the right amount of curvature. Here we propose Hyperbolic Graph Convolutional Neural Network (HGCN), the first inductive hyperbolic GCN that leverages both the expressiveness of GCNs and hyperbolic geometry to learn inductive node representations for hierarchical and scale-free graphs. We derive GCNs operations in the hyperboloid model of hyperbolic space and map Euclidean input features to embeddings in hyperbolic spaces with different trainable curvature at each layer. Experiments demonstrate that HGCN learns embeddings that preserve hierarchical structure, and leads to improved performance when compared to Euclidean analogs, even with very low dimensional embeddings: compared to state-of-the-art GCNs, HGCN achieves an error reduction of up to 63.1%more »in ROC AUC for link prediction and of up to 47.5% in F1 score for node classification, also improving state-of-the art on the PubMed dataset.« less
5. FACS-GCN: Fairness-Aware Cost-Sensitive Boosting of Graph Convolutional Networks

   https://doi.org/10.1109/IJCNN55064.2022.9892919  

   Santos, Francisco ; Ye, Junke ; Masrour, Farzan ; Tan, Pang-Ning ; Esfahanian, Abdol-Hossein ( July 2022 , Proceedings of the 2022 International Joint Conference on Neural Networks (IJCNN))

   Graph neural networks (GNNs) have emerged as a powerful tool for modeling graph data due to their ability to learn a concise representation of the data by integrating the node attributes and link information in a principled fashion. However, despite their promise, there are several practical challenges that must be overcome to effectively use them for node classification problems. In particular, current approaches are vulnerable to different kinds of biases inherent in the graph data. First, if the class distribution is imbalanced, then the GNNs' loss function is biased towards classifying the majority class correctly rather than the minority class, which hurts the performance of the latter class. Second, due to homophily effect, the learned representation and subsequent downstream tasks may favor certain demographic groups over others when applied to social network data. To mitigate such biases, we propose a novel framework called Fairness-Aware Cost Sensitive Graph Convolutional Network (FACS-GCN) for classifying nodes in networks with skewed class distributions. Our approach combines a cost-sensitive exponential loss with an adversarial learning component to alleviate the ill-effects of both biases. The framework employs a stagewise additive modeling approach to ensure there is no significant loss in accuracy when imparting fairness into themore »GNN. Experimental results on 6 benchmark graph data demonstrate the effectiveness of FACS-GCN against comparable baseline methods in terms of promoting fairness while maintaining a high model accuracy on the majority of the datasets.« less