Multi-Facet Network Embedding: Beyond the General Solution of Detection and Representation

In network analysis, community detection and network embedding are two important topics. Community detection tends to obtain the most noticeable partition, while network embedding aims at seeking node representations which contains as many diverse properties as possible. We observe that the current community detection and network embedding problems are being resolved by a general solution, i.e., "maximizing the consistency between similar nodes while maximizing the distance between the dissimilar nodes." This general solution only exploits the most noticeable structure (facet) of the network, which effectively satisfies the demands of the community detection. Unfortunately, most of the specific embedding algorithms, which are developed from the general solution, cannot achieve the goal of network embedding by exploring only one facet of the network. To improve the general solution for better modeling the real network, we propose a novel network embedding method, Multi-facet Network Embedding (MNE), to capture the multiple facets of the network. MNE learns multiple embeddings simultaneously, with the Hilbert Schmidt Independence Criterion (HSIC) being the a diversity constraint. To efficiently solve the optimization problem, we propose a Binary HSIC with linear complexity and solve the MNE objective function by adopting the Augmented Lagrange Multiplier (ALM) method. The overall complexity is linear with the scale of the network. Extensive results demonstrate that MNE gives efficient performances and outperforms the state-of-the-art network embedding methods