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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. 

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2. Learning Similarity-Preserving Representations of Brain Structure-Function Coupling

   https://doi.org/10.23919/EUSIPCO55093.2022.9909566  

   Li, Yang; Mateos, Gonzalo (August 2022, 2022 30th European Signal Processing Conference (EUSIPCO))

   Advances in graph signal processing for network neuroscience offer a unique pathway to integrate brain structure and function, with the goal of revealing some of the brain's organizing principles at the system level. In this direction, we develop a supervised graph representation learning framework to model the relationship between brain structural connectivity (SC) and functional connectivity (FC) via a graph encoder-decoder system. Specifically, we propose a Siamese network architecture equipped with graph convolutional encoders to learn graph (i.e., subject)-level embeddings that preserve application-dependent similarity measures between brain networks. This way, we effectively increase the number of training samples and bring in the flexibility to incorporate additional prior information via the prescribed target graph-level distance. While information on the brain structure-function coupling is implicitly distilled via reconstruction of brain FC from SC, our model also manages to learn representations that preserve the similarity between input graphs. The superior discriminative power of the learnt representations is demonstrated in downstream tasks including subject classification and visualization. All in all, this work advocates the prospect of leveraging learnt graph-level, similarity-preserving embeddings for brain network analysis, by bringing to bear standard tools of metric data analysis. 

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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. 

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4. 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 datasets 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. 

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5. Classifying Subjects with PFC Lesions from Healthy Controls during Working Memory Encoding via Graph Convolutional Networks

   https://doi.org/10.1109/NER52421.2023.10123793  

   Balaji, Sai Sanjay; Parhi, Keshab K. (April 2023, 2023 11th International IEEE/EMBS Conference on Neural Engineering (NER))

   This paper describes a group-level classification of 14 patients with prefrontal cortex (pFC) lesions from 20 healthy controls using multi-layer graph convolutional networks (GCN) with features inferred from the scalp EEG recorded from the encoding phase of working memory (WM) trials. We first construct undirected and directed graphs to represent the WM encoding for each trial for each subject using distance correlation- based functional connectivity measures and differential directed information-based effective connectivity measures, respectively. Centrality measures of betweenness centrality, eigenvector centrality, and closeness centrality are inferred for each of the 64 channels from the brain connectivity. Along with the three centrality measures, each graph uses the relative band powers in the five frequency bands - delta, theta, alpha, beta, and gamma- as node features. The summarized graph representation is learned using two layers of GCN followed by mean pooling, and fully connected layers are used for classification. The final class label for a subject is decided using majority voting based on the results from all the subject's trials. The GCN-based model can correctly classify 28 of the 34 subjects (82.35% accuracy) with undirected edges represented by functional connectivity measure of distance correlation and classify all 34 subjects (100% accuracy) with directed edges characterized by effective connectivity measure of differential directed information. 

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