Embedding network data into a low-dimensional vector space has shown promising performance for many real-world applications, such as node classification and entity retrieval. However, most existing methods focused only on leveraging network structure. For social networks, besides the network structure, there also exists rich information about social actors, such as user profiles of friendship networks and textual content of citation networks. These rich attribute information of social actors reveal the homophily effect, exerting huge impacts on the formation of social networks. In this paper, we explore the rich evidence source of attributes in social networks to improve network embedding. We propose a generic Social Network Embedding framework (SNE), which learns representations for social actors (i.e., nodes) by preserving both the structural proximity and attribute proximity. While the structural proximity captures the global network structure, the attribute proximity accounts for the homophily effect. To justify our proposal, we conduct extensive experiments on four real-world social networks. Compared to the state-of-the-art network embedding approaches, SNE can learn more informative representations, achieving substantial gains on the tasks of link prediction and node classification. Specifically, SNE significantly outperforms node2vec with an 8.2 relative improvement on the link prediction task, and a 12.7 gain on the node classification task.
Some earlier works such as Local Linear Embedding (LLE) @cite_2 , IsoMAP @cite_12 and Laplacian Eigenmap @cite_25 first transform data into an affinity graph based on the feature vectors of nodes ( e.g., k-nearest neighbors of nodes) and then embed the graph by solving the leading eigenvectors of the affinity matrix.
@cite_25 @cite_12 @cite_2
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Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a higher dimensional space. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering. Several applications are considered. Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data. Here, we introduce locally linear embedding (LLE), an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. Unlike clustering methods for local dimensionality reduction, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve local minima. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds, such as those generated by images of faces or documents of text. How do we judge similarity? Our mental representations of the world are formed by processing large numbers of sensory in