Many successful methods have been proposed for learning low dimensional representations on large-scale networks, while almost all existing methods are designed in inseparable processes, learning embeddings for entire networks even when only a small proportion of nodes are of interest. This leads to great inconvenience, especially on super-large or dynamic networks, where these methods become almost impossible to implement. In this paper, we formalize the problem of separated matrix factorization, based on which we elaborate a novel objective function that preserves both local and global information. We further propose SepNE, a simple and flexible network embedding algorithm which independently learns representations for different subsets of nodes in separated processes. By implementing separability, our algorithm reduces the redundant efforts to embed irrelevant nodes, yielding scalability to super-large networks, automatic implementation in distributed learning and further adaptations. We demonstrate the effectiveness of this approach on several real-world networks with different scales and subjects. With comparable accuracy, our approach significantly outperforms state-of-the-art baselines in running times on large networks.

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Graph Neural Networks (GNNs) have recently been used for node and graph classification tasks with great success, but GNNs model dependencies among the attributes of nearby neighboring nodes rather than dependencies among observed node labels. In this work, we consider the task of inductive node classification using GNNs in supervised and semi-supervised settings, with the goal of incorporating label dependencies. Because current GNNs are not universal (i.e., most-expressive) graph representations, we propose a general collective learning approach to increase the representation power of any existing GNN. Our framework combines ideas from collective classification with self-supervised learning, and uses a Monte Carlo approach to sampling embeddings for inductive learning across graphs. We evaluate performance on five real-world network datasets and demonstrate consistent, significant improvement in node classification accuracy, for a variety of state-of-the-art GNNs.

Network embedding aims to learn a latent, low-dimensional vector representations of network nodes, effective in supporting various network analytic tasks. While prior arts on network embedding focus primarily on preserving network topology structure to learn node representations, recently proposed attributed network embedding algorithms attempt to integrate rich node content information with network topological structure for enhancing the quality of network embedding. In reality, networks often have sparse content, incomplete node attributes, as well as the discrepancy between node attribute feature space and network structure space, which severely deteriorates the performance of existing methods. In this paper, we propose a unified framework for attributed network embedding-attri2vec-that learns node embeddings by discovering a latent node attribute subspace via a network structure guided transformation performed on the original attribute space. The resultant latent subspace can respect network structure in a more consistent way towards learning high-quality node representations. We formulate an optimization problem which is solved by an efficient stochastic gradient descent algorithm, with linear time complexity to the number of nodes. We investigate a series of linear and non-linear transformations performed on node attributes and empirically validate their effectiveness on various types of networks. Another advantage of attri2vec is its ability to solve out-of-sample problems, where embeddings of new coming nodes can be inferred from their node attributes through the learned mapping function. Experiments on various types of networks confirm that attri2vec is superior to state-of-the-art baselines for node classification, node clustering, as well as out-of-sample link prediction tasks. The source code of this paper is available at https://github.com/daokunzhang/attri2vec.

Network representation learning in low dimensional vector space has attracted considerable attention in both academic and industrial domains. Most real-world networks are dynamic with addition/deletion of nodes and edges. The existing graph embedding methods are designed for static networks and they cannot capture evolving patterns in a large dynamic network. In this paper, we propose a dynamic embedding method, dynnode2vec, based on the well-known graph embedding method node2vec. Node2vec is a random walk based embedding method for static networks. Applying static network embedding in dynamic settings has two crucial problems: 1) Generating random walks for every time step is time consuming 2) Embedding vector spaces in each timestamp are different. In order to tackle these challenges, dynnode2vec uses evolving random walks and initializes the current graph embedding with previous embedding vectors. We demonstrate the advantages of the proposed dynamic network embedding by conducting empirical evaluations on several large dynamic network datasets.

The key issue of few-shot learning is learning to generalize. In this paper, we propose a large margin principle to improve the generalization capacity of metric based methods for few-shot learning. To realize it, we develop a unified framework to learn a more discriminative metric space by augmenting the softmax classification loss function with a large margin distance loss function for training. Extensive experiments on two state-of-the-art few-shot learning models, graph neural networks and prototypical networks, show that our method can improve the performance of existing models substantially with very little computational overhead, demonstrating the effectiveness of the large margin principle and the potential of our method.

Network embedding has become a hot research topic recently which can provide low-dimensional feature representations for many machine learning applications. Current work focuses on either (1) whether the embedding is designed as an unsupervised learning task by explicitly preserving the structural connectivity in the network, or (2) whether the embedding is a by-product during the supervised learning of a specific discriminative task in a deep neural network. In this paper, we focus on bridging the gap of the two lines of the research. We propose to adapt the Generative Adversarial model to perform network embedding, in which the generator is trying to generate vertex pairs, while the discriminator tries to distinguish the generated vertex pairs from real connections (edges) in the network. Wasserstein-1 distance is adopted to train the generator to gain better stability. We develop three variations of models, including GANE which applies cosine similarity, GANE-O1 which preserves the first-order proximity, and GANE-O2 which tries to preserves the second-order proximity of the network in the low-dimensional embedded vector space. We later prove that GANE-O2 has the same objective function as GANE-O1 when negative sampling is applied to simplify the training process in GANE-O2. Experiments with real-world network datasets demonstrate that our models constantly outperform state-of-the-art solutions with significant improvements on precision in link prediction, as well as on visualizations and accuracy in clustering tasks.

Network embedding has attracted considerable research attention recently. However, the existing methods are incapable of handling billion-scale networks, because they are computationally expensive and, at the same time, difficult to be accelerated by distributed computing schemes. To address these problems, we propose RandNE, a novel and simple billion-scale network embedding method. Specifically, we propose a Gaussian random projection approach to map the network into a low-dimensional embedding space while preserving the high-order proximities between nodes. To reduce the time complexity, we design an iterative projection procedure to avoid the explicit calculation of the high-order proximities. Theoretical analysis shows that our method is extremely efficient, and friendly to distributed computing schemes without any communication cost in the calculation. We demonstrate the efficacy of RandNE over state-of-the-art methods in network reconstruction and link prediction tasks on multiple datasets with different scales, ranging from thousands to billions of nodes and edges.

Adding attributes for nodes to network embedding helps to improve the ability of the learned joint representation to depict features from topology and attributes simultaneously. Recent research on the joint embedding has exhibited a promising performance on a variety of tasks by jointly embedding the two spaces. However, due to the indispensable requirement of globality based information, present approaches contain a flaw of in-scalability. Here we propose \emph{SANE}, a scalable attribute-aware network embedding algorithm with locality, to learn the joint representation from topology and attributes. By enforcing the alignment of a local linear relationship between each node and its K-nearest neighbors in topology and attribute space, the joint embedding representations are more informative comparing with a single representation from topology or attributes alone. And we argue that the locality in \emph{SANE} is the key to learning the joint representation at scale. By using several real-world networks from diverse domains, We demonstrate the efficacy of \emph{SANE} in performance and scalability aspect. Overall, for performance on label classification, SANE successfully reaches up to the highest F1-score on most datasets, and even closer to the baseline method that needs label information as extra inputs, compared with other state-of-the-art joint representation algorithms. What's more, \emph{SANE} has an up to 71.4\% performance gain compared with the single topology-based algorithm. For scalability, we have demonstrated the linearly time complexity of \emph{SANE}. In addition, we intuitively observe that when the network size scales to 100,000 nodes, the "learning joint embedding" step of \emph{SANE} only takes $\approx10$ seconds.

Adding attributes for nodes to network embedding helps to improve the ability of the learned joint representation to depict features from topology and attributes simultaneously. Recent research on the joint embedding has exhibited a promising performance on a variety of tasks by jointly embedding the two spaces. However, due to the indispensable requirement of globality based information, present approaches contain a flaw of in-scalability. Here we propose \emph{SANE}, a scalable attribute-aware network embedding algorithm with locality, to learn the joint representation from topology and attributes. By enforcing the alignment of a local linear relationship between each node and its K-nearest neighbors in topology and attribute space, the joint embedding representations are more informative comparing with a single representation from topology or attributes alone. And we argue that the locality in \emph{SANE} is the key to learning the joint representation at scale. By using several real-world networks from diverse domains, We demonstrate the efficacy of \emph{SANE} in performance and scalability aspect. Overall, for performance on label classification, SANE successfully reaches up to the highest F1-score on most datasets, and even closer to the baseline method that needs label information as extra inputs, compared with other state-of-the-art joint representation algorithms. What's more, \emph{SANE} has an up to 71.4\% performance gain compared with the single topology-based algorithm. For scalability, we have demonstrated the linearly time complexity of \emph{SANE}. In addition, we intuitively observe that when the network size scales to 100,000 nodes, the "learning joint embedding" step of \emph{SANE} only takes $\approx10$ seconds.

Network embedding represents nodes in a continuous vector space and preserves structure information from the Network. Existing methods usually adopt a "one-size-fits-all" approach when concerning multi-scale structure information, such as first- and second-order proximity of nodes, ignoring the fact that different scales play different roles in the embedding learning. In this paper, we propose an Attention-based Adversarial Autoencoder Network Embedding(AAANE) framework, which promotes the collaboration of different scales and lets them vote for robust representations. The proposed AAANE consists of two components: 1) Attention-based autoencoder effectively capture the highly non-linear network structure, which can de-emphasize irrelevant scales during training. 2) An adversarial regularization guides the autoencoder learn robust representations by matching the posterior distribution of the latent embeddings to given prior distribution. This is the first attempt to introduce attention mechanisms to multi-scale network embedding. Experimental results on real-world networks show that our learned attention parameters are different for every network and the proposed approach outperforms existing state-of-the-art approaches for network embedding.

Social network analysis provides meaningful information about behavior of network members that can be used for diverse applications such as classification, link prediction. However, network analysis is computationally expensive because of feature learning for different applications. In recent years, many researches have focused on feature learning methods in social networks. Network embedding represents the network in a lower dimensional representation space with the same properties which presents a compressed representation of the network. In this paper, we introduce a novel algorithm named "CARE" for network embedding that can be used for different types of networks including weighted, directed and complex. Current methods try to preserve local neighborhood information of nodes, whereas the proposed method utilizes local neighborhood and community information of network nodes to cover both local and global structure of social networks. CARE builds customized paths, which are consisted of local and global structure of network nodes, as a basis for network embedding and uses the Skip-gram model to learn representation vector of nodes. Subsequently, stochastic gradient descent is applied to optimize our objective function and learn the final representation of nodes. Our method can be scalable when new nodes are appended to network without information loss. Parallelize generation of customized random walks is also used for speeding up CARE. We evaluate the performance of CARE on multi label classification and link prediction tasks. Experimental results on various networks indicate that the proposed method outperforms others in both Micro and Macro-f1 measures for different size of training data.

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