Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. While achieving competitive performance on a variety of network inference tasks such as node classification and link prediction, these methods treat the relations between nodes as a binary variable and ignore the rich semantics of edges. In this work, we attempt to learn network embeddings which simultaneously preserve network structure and relations between nodes. Experiments on several real-world networks illustrate that by considering different relations between different node pairs, our method is capable of producing node embeddings of higher quality than a number of state-of-the-art network embedding methods, as evaluated on a challenging multi-label node classification task.
Unsupervised network embedding methods only utilize network structure information to construct node embeddings. The learned node embeddings are treated as generic feature vectors, which can then be used for downstream tasks in networks. A representative method is DeepWalk @cite_3 , which is a two-phase method for learning node embeddings. In the first step, DeepWalk constructs node neighborhoods by performing fixed-length random walks in the input network. Then, DeepWalk employs the skip-gram @cite_0 model to preserve the co-occurrences between nodes and their neighbors. Many later studies follow this two-step framework for learning network embeddings, by proposing different strategies for constructing node neighborhoods @cite_16 @cite_17 or modeling co-occurrences between nodes @cite_9 @cite_10 .
@cite_9 @cite_3 @cite_0 @cite_16 @cite_10 @cite_17
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We present DeepWalk, a novel approach for learning latent representations of vertices in a network. These latent representations encode social relations in a continuous vector space, which is easily exploited by statistical models. DeepWalk generalizes recent advancements in language modeling and unsupervised feature learning (or deep learning) from sequences of words to graphs. DeepWalk uses local information obtained from truncated random walks to learn latent representations by treating walks as the equivalent of sentences. We demonstrate DeepWalk's latent representations on several multi-label network classification tasks for social networks such as BlogCatalog, Flickr, and YouTube. Our results show that DeepWalk outperforms challenging baselines which are allowed a global view of the network, especially in the presence of missing information. DeepWalk's representations can provide F1 scores up to 10 higher than competing methods when labeled data is sparse. In some experiments, DeepWalk's representations are able to outperform all baseline methods while using 60 less training data. DeepWalk is also scalable. It is an online learning algorithm which builds useful incremental results, and is trivially parallelizable. These qualities make it suitable for a broad class of real world applications such as network classification, and anomaly detection. DeepWalk is a typical representation learning method that learns low-dimensional representations for vertices in social networks. Similar to other network representation learning (NRL) models, it encodes the network structure into vertex representations and is learnt in unsupervised form. However, the learnt representations usually lack the ability of discrimination when applied to machine learning tasks, such as vertex classification. In this paper, we overcome this challenge by proposing a novel semi-supervised model, max-margin Deep-Walk (MMDW). MMDW is a unified NRL framework that jointly optimizes the max-margin classifier and the aimed social representation learning model. Influenced by the max-margin classifier, the learnt representations not only contain the network structure, but also have the characteristic of discrimination. The visualizations of learnt representations indicate that our model is more discriminative than unsupervised ones, and the experimental results on vertex classification demonstrate that our method achieves a significant improvement than other state-of-the-art methods. The source code can be obtained from https: github.com thunlp MMDW. Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factorization framework with closed forms. Our analysis and proofs reveal that: (1) DeepWalk empirically produces a low-rank transformation of a network's normalized Laplacian matrix; (2) LINE, in theory, is a special case of DeepWalk when the size of vertices' context is set to one; (3) As an extension of LINE, PTE can be viewed as the joint factorization of multiple networks» Laplacians; (4) node2vec is factorizing a matrix related to the stationary distribution and transition probability tensor of a 2nd-order random walk. We further provide the theoretical connections between skip-gram based network embedding algorithms and the theory of graph Laplacian. Finally, we present the NetMF method as well as its approximation algorithm for computing network embedding. Our method offers significant improvements over DeepWalk and LINE for conventional network mining tasks. This work lays the theoretical foundation for skip-gram based network embedding methods, leading to a better understanding of latent network representation learning. Network embedding is an important method to learn low-dimensional representations of vertexes in networks, aiming to capture and preserve the network structure. Almost all the existing network embedding methods adopt shallow models. However, since the underlying network structure is complex, shallow models cannot capture the highly non-linear network structure, resulting in sub-optimal network representations. Therefore, how to find a method that is able to effectively capture the highly non-linear network structure and preserve the global and local structure is an open yet important problem. To solve this problem, in this paper we propose a Structural Deep Network Embedding method, namely SDNE. More specifically, we first propose a semi-supervised deep model, which has multiple layers of non-linear functions, thereby being able to capture the highly non-linear network structure. Then we propose to exploit the first-order and second-order proximity jointly to preserve the network structure. The second-order proximity is used by the unsupervised component to capture the global network structure. While the first-order proximity is used as the supervised information in the supervised component to preserve the local network structure. By jointly optimizing them in the semi-supervised deep model, our method can preserve both the local and global network structure and is robust to sparse networks. Empirically, we conduct the experiments on five real-world networks, including a language network, a citation network and three social networks. The results show that compared to the baselines, our method can reconstruct the original network significantly better and achieves substantial gains in three applications, i.e. multi-label classification, link prediction and visualization.