Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec

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.Comment: 9 pages, published in WSDM 2018 proceeding

Deep Representation Learning for Social Network Analysis

Social network analysis is an important problem in data mining. A fundamental step for analyzing social networks is to encode network data into low-dimensional representations, i.e., network embeddings, so that the network topology structure and other attribute information can be effectively preserved. Network representation leaning facilitates further applications such as classification, link prediction, anomaly detection and clustering. In addition, techniques based on deep neural networks have attracted great interests over the past a few years. In this survey, we conduct a comprehensive review of current literature in network representation learning utilizing neural network models. First, we introduce the basic models for learning node representations in homogeneous networks. Meanwhile, we will also introduce some extensions of the base models in tackling more complex scenarios, such as analyzing attributed networks, heterogeneous networks and dynamic networks. Then, we introduce the techniques for embedding subgraphs. After that, we present the applications of network representation learning. At the end, we discuss some promising research directions for future work