Network embedding which is to learn a low dimensional representation of nodes in a network has been used in many network analysis tasks. Some network embedding methods, including those based on Generative Adversarial Networks (GAN) (a promising deep learning model), have been proposed recently. Existing GAN-based methods typically use GAN to learn a Gaussian distribution as a prior for network embedding, which makes it difficult to distinguish the node representation from Gaussian distribution. It did not apply the adversarial learning strategy on the representation mechanism but just on representation results. Thus, it does not make full use of the essential advantage of GAN, and leads to compromised performance of the method. To address this problem, we propose a novel adversarial learning framework consisting of three players for network embedding, which applies the adversarial learning strategy on the representation mechanism, called Adversarial representation mechanism GAN (ArmGAN). Specifically, the first two players, named encoder and competitor, aim to learn two different representation mechanisms (i.e., two ways projecting data onto latent space). They compete with each other to improve their representation mechanisms. The third player is the discriminator, which discriminate the representation mechanism of the encoder from that of the competitor. In addition, we design a perturbation strategy to produce fake networks from the original network, and feed the fake networks to the competitor to obtain a “fake” representation mechanism. We evaluated ArmGAN on a variety of tasks including node clustering, node classification, link prediction and visualization. Moreover, we compared ArmGAN with 10 state-of-the-art methods (including DGI, which is well-known for its high accuracy) on 7 real-world networks. The experimental results show the significant superiority of ArmGAN over the existing methods.

Most of the existing Graph Neural Networks (GNNs) are deliberately designed for semi-supervised learning tasks, where supervision information (labelled node) is utilized to mitigate the oversmoothing problem of message passing. Unfortunately, the oversmoothing problem tends to be more severe in unsupervised tasks, since supervision information is not available. Since community structure/cluster is an essential characteristic of network, a natural approach to reduce the oversmoothing problem is to also constrain the node embeddings to maintain their own characteristics to prevent all the node embeddings from becoming too similar to be distinguished. In this paper, a novel Optimal Transport based Graph Neural Network (OT-GNN) is proposed to overcome the oversmoothing problem in unsupervised GNNs by imposing the equal-sized clustering constraints to the obtained node embeddings. To solve the combinatorial optimization problem, the constrained objective function of unsupervised GNN is relaxed to an Optimal Transport problem, and a fast version of the Sinkhorm-Knopp algorithm is adopted to handle large networks. Extensive experiments on node clustering and classification demonstrate the superior performance of our proposed OT-GNN.

Network embedding which is to learn a low dimensional representation of nodes in a network has been used in many network analysis tasks. Some network embedding methods, including those based on generative adversarial networks (GAN) (a promising deep learning technique), have been proposed recently. Existing GAN-based methods typically use GAN to learn a Gaussian distribution as a priori for network embedding. However, this strategy makes it difficult to distinguish the node representation from Gaussian distribution. Moreover, it does not make full use of the essential advantage of GAN (that is to adversarially learn the representation mechanism rather than the representation itself), leading to compromised performance of the method. To address this problem, we propose to use the adversarial idea on the representation mechanism, i.e. on the encoding mechanism under the framework of autoencoder. Specifically, we use the mutual information between node attributes and embedding as a reasonable alternative of this encoding mechanism (which is much easier to track). Additionally, we introduce another mapping mechanism (which is based on GAN) as a competitor into the adversarial learning system. A range of empirical results demonstrate the effectiveness of the proposed approach.

The purpose of network embedding is to learn a low-dimensional representation for each node in the network. One can then use this low-dimensional representation to solve some network analysis tasks, such as node classification and node clustering. At present, there are several network embedding learning methods based on GAN (Generative Adversarial Networks) to enhance the robustness of representations. However, these methods have two drawbacks. First, they are often too difficult to be trained stably. Second, they only learn the robust representations by matching the posterior distribution of the latent representations to the given priors. On the contrary, Capsule Networks can learn a more equivariant representation of images that is more robust to the changes in pose and spatial relationships of parts of objects in images. However, there is still no research using Capsule Network for network embedding since the social network is essentially different from images. For this problem, we propose a new approach of adversarial capsule learning (ACL) for network embedding, which is the first time to use Capsule Network in the network analysis tasks. To be specific, the new model consists of two parts, a generator and discriminator. We use Graph Convolutional Networks (GCN) as the generator to learn the embedding of nodes, and use Capsule Network as the discriminator to distinguish between the real and fake samples as accurately as possible. The experimental results demonstrate the effectiveness of the proposed new method.