Role-based network embedding aims to map network into low-dimensional node representations while preserving structural similarities. Adjacency matrix contain both the local and global information of a network, but it cannot directly represent the role of nodes. So it is essential to extract higher-order structural features from adjacency matrix for role-based network embedding (structural equivalence). While being sensitive to noise in real networks in general, the features extracted by some identical methods cannot truly represent the role of nodes. Therefore, we propose a deep learning framework RESD . In detail, we first propose extracting higher-order structural features for each node in the network. Then, we utilize the Variational Auto-Encoder (VAE) to model the nonlinear relationship of the features, reduce noise and improve the robustness of embedding. Furthermore, in the embedding space, we apply a degree-regularized constraint to guide the representation learning for preserving key structural information of nodes (e.g., degrees), which may be lost due to the principle of VAE framework. Finally, we construct a unified objective function to learn the node embedding for role discovery by preserving the structural features and node degree. We compare our model with several state-of-the-art methods on real-world networks. The results of extensive experiments demonstrate the effectiveness of our model and prove that our model scales well with dimension and network size.

Role-based network embedding via structural features reconstruction with degree-regularized constraint

Task fMRI provides an opportunity to analyze the working mechanisms of the human brain during specific experimental paradigms. Deep learning models have increasingly been applied for decoding and encoding purposes study to representations in task fMRI data. More recently, graph neural networks, or neural networks models designed to leverage the properties of graph representations, have recently shown promise in task fMRI decoding studies. Here, we propose an end-to-end graph convolutional network (GCN) framework with three convolutional layers to classify task fMRI data from the Human Connectome Project dataset. We compared the predictive performance of our GCN model across four of the most widely used node embedding algorithms—NetMF, RandNE, Node2Vec, and Walklets—to automatically extract the structural properties of the nodes in the functional graph. The empirical results indicated that our GCN framework accurately predicted individual differences (0.978 and 0.976) with the NetMF and RandNE embedding methods, respectively. Furthermore, to assess the effects of individual differences, we tested the classification performance of the model on sub-datasets divided according to gender and fluid intelligence. Experimental results indicated significant differences in the classification predictions of gender, but not high/low fluid intelligence fMRI data. Our experiments yielded promising results and demonstrated the superior ability of our GCN in modeling task fMRI data.

/pdf/decoding-task-based-fmri-data-with-graph-neural-networks-3os9osdc.pdf

Decoding Task-Based fMRI Data with Graph Neural Networks, Considering Individual Differences

Understanding the evolutionary patterns of real-world complex systems such as human interactions, biological interactions, transport networks, and computer networks is important for our daily lives. Predicting future links among the nodes in these dynamic networks has many practical implications. This research aims to enhance our understanding of the evolution of networks by formulating and solving the link-prediction problem for temporal networks using graph representation learning as an advanced machine learning approach. Learning useful representations of nodes in these networks provides greater predictive power with less computational complexity and facilitates the use of machine learning methods. Considering that existing models fail to consider the temporal dimensions of the networks, this research proposes a novel temporal network-embedding algorithm for graph representation learning. This algorithm generates low-dimensional features from large, high-dimensional networks to predict temporal patterns in dynamic networks. The proposed algorithm includes a new dynamic node-embedding algorithm that exploits the evolving nature of the networks by considering a simple three-layer graph neural network at each time step and extracting node orientation by using Given's angle method. Our proposed temporal network-embedding algorithm, TempNodeEmb, is validated by comparing it to seven state-of-the-art benchmark network-embedding models. These models are applied to eight dynamic protein-protein interaction networks and three other real-world networks, including dynamic email networks, online college text message networks, and human real contact datasets. To improve our model, we have considered time encoding and proposed another extension to our model, TempNodeEmb++. The results show that our proposed models outperform the state-of-the-art models in most cases based on two evaluation metrics. 

/pdf/a-novel-temporal-network-embedding-algorithm-for-link-3iiv2m43.pdf

A Novel Temporal Network-Embedding Algorithm for Link Prediction in Dynamic Networks

Graph embedding is a general approach to tackling graph-analytic problems by encoding nodes into low-dimensional representations. Most existing embedding methods are transductive since the information of all nodes is required in training, including those to be predicted. In this paper, we propose a novel inductive embedding method for semi-supervised learning on graphs. This method generates node representations by learning a parametric function to aggregate information from the neighborhood using an attention mechanism, and hence naturally generalizes to previously unseen nodes. Furthermore, adversarial training serves as an external regularization enforcing the learned representations to match a prior distribution for improving robustness and generalization ability. Experiments on real-world clean or noisy graphs are used to demonstrate the effectiveness of this approach.

Adversarially Regularized Graph Attention Networks for Inductive Learning on Partially Labeled Graphs.

Newly arriving nodes in dynamics networks would gradually make the node embedding space drifted and the retraining of node embedding and downstream models indispensable. An exact threshold size of these new nodes, below which the node embedding space will be predicatively maintained, however, is rarely considered in either theory or experiment. From the view of matrix perturbation theory, a threshold of the maximum number of new nodes that keep the node embedding space approximately equivalent is analytically provided and empirically validated. It is therefore theoretically guaranteed that as the size of newly arriving nodes is below this threshold, embeddings of these new nodes can be quickly derived from embeddings of original nodes. A generation framework, Space-Invariant Projection (SIP), is accordingly proposed to enables arbitrary static MF-based embedding schemes to embed new nodes in dynamics networks fast. The time complexity of SIP is linear with the network size. By combining SIP with four state-of-the-art MF-based schemes, we show that SIP exhibits not only wide adaptability but also strong empirical performance in terms of efficiency and efficacy on the node classification task in three real datasets.

pdf/space-invariant-projection-in-streaming-network-embedding-2amv96al.pdf

Space-Invariant Projection in Streaming Network Embedding

In recent years, network embedding has attracted extensive interests, which aims at representing nodes of an original network in a low-dimensional vector space while preserving the inherent topological structures of the network. Despite the remarkable advantages of complex networks, most existing network embedding methods are mainly focused on static networks while ignoring the evolving characteristic, which is proved to be an essential property of real-world networks. In this paper, we propose Node Proximity Preserved Dynamic Network Embedding via Matrix Perturbation (NPDNE) to tackle the dilemma. Specifically, our method implements a low-rank transformation on the normalized Laplacian matrix of the given networks and then derives the embedding vectors through generalized SVD. Subsequently, the node proximities are preserved in the embedding vectors by exploiting the eigen-decomposition reweighing theorem, which reveals the intrinsic relationship among different-order proximities. Moreover, a generalized eigen perturbation is adopted to update the embedding vectors so that the evolution of given networks can be captured over time. Finally, we conduct experiments of multi-label classification, link prediction, and visualization on several real-world datasets. The experimental results demonstrate the superiority of the proposed NPDNE model compared with state-of-the-art baselines.

Node proximity preserved dynamic network embedding via matrix perturbation

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Node proximity preserved dynamic network embedding via matrix perturbation