text: Real-world social networks and digital platforms are comprised of individuals (nodes) that are linked to other individuals or entities through multiple types of relationships (links). Sub-networks of such a network based on each type of link correspond to distinct views of the underlying network. In real-world applications, each node is typically linked to only a small subset of other nodes. Hence, practical approaches to problems such as node labeling have to cope with the resulting sparse networks. While low-dimensional network embeddings offer a promising approach to this problem, most of the current network embedding methods focus primarily on single view networks. We introduce a novel multi-view network embedding (MVNE) algorithm for constructing low-dimensional node embeddings from multi-view networks. MVNE adapts and extends an approach to single view network embedding (SVNE) using graph factorization clustering (GFC) to the multi-view setting using an objective function that maximizes the agreement between views based on both the local and global structure of the underlying multi-view graph. Our experiments with several benchmark real-world single view networks show that GFC-based SVNE yields network embeddings that are competitive with or superior to those produced by the state-of-the-art single view network embedding methods when the embeddings are used for labeling unlabeled nodes in the networks. Our experiments with several multi-view networks show that MVNE substantially outperforms the single view methods on integrated view and the state-of-the-art multi-view methods. We further show that even when the goal is to predict labels of nodes within a single target view, MVNE outperforms its single-view counterpart suggesting that the MVNE is able to extract the information that is useful for labeling nodes in the target view from the all of the views.
  @cite_28: Network embedding aims to learn a low-dimensional vector representation (or embedding) for each node in the social and information networks, with the constraint to preserve network structures. Most existing methods focus on single network embedding, ignoring the relationship between multiple networks. In many real-world applications, however, related multiple networks (e.g., social networks from different platforms) may contain complementary information which can lead to further refined node embeddings. Thus, in this paper, we propose a novel multi-network embedding method, DMNE. DMNE is flexible, which allows different networks to have different sizes, to be (un)weighted and (un)directed. It leverages multiple networks via cross-network relationships between nodes in different networks, which may form many-to-many node mappings, and be associated with weights. To model the non-linearity of the network data, we develop DMNE to have a new deep learning architecture, which coordinates multiple neural networks (one for each input network data) with a co-regularized loss function to manipulate cross-network relationships. With multiple layers of non-linear mappings, DMNE progressively transforms each input network into a highly non-linear latent space, and in the meantime, adapts different latent spaces to each other through a co-regularized learning schema. Extensive experimental results on four real-life datasets demonstrate the effectiveness of our method.
  @cite_34: 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.
  @cite_7: We propose a simple clustering framework on graphs encoding pairwise data similarities. Unlike usual similarity-based methods, the approach softly assigns data to clusters in a probabilistic way. More importantly, a hierarchical clustering is naturally derived in this framework to gradually merge lower-level clusters into higher-level ones. A random walk analysis indicates that the algorithm exposes clustering structures in various resolutions, i.e., a higher level statistically models a longer-term diffusion on graphs and thus discovers a more global clustering structure. Finally we provide very encouraging experimental results.
  @cite_17: We investigate an unsupervised generative approach for network embedding. A multi-task Siamese neural network structure is formulated to connect embedding vectors and our objective to preserve the global node ranking and local proximity of nodes. We provide deeper analysis to connect the proposed proximity objective to link prediction and community detection in the network. We show our model can satisfy the following design properties: scalability, asymmetry, unity and simplicity. Experiment results not only verify the above design properties but also demonstrate the superior performance in learning-to-rank, classification, regression, and link prediction tasks.
summary: In contrast to the existing multi-view network embedding methods, MVNE exploits a recently discovered connection between network adjacency matrix factorization and network embedding @cite_34 to utilize GFC @cite_7 , a graph factorization method, to perform single view network embedding. MVNE extends the resulting single view network embedding algorithm to the multi-view setting. Inspired by @cite_17 , MVNE uses a novel objective function that maximizes the agreement between views while combining information derived from the local as well as the global structure of the underlying multi-view networks. Like DMNE @cite_28 , MVNE uses a co-regularized objective function to maximize the agreement in the embedding space and to control the embedding dimension. Unlike DMNE which requires on computationally expensive training of a deep neural network, MVNE is considerably more efficient and hence scalable to large networks.