Hierarchical Community Structure Preserving Network Embedding: A Subspace Approach

To depict ubiquitous relational data in real world, network data are widely applied in modeling complex relationships. Projecting vertices to low dimensional spaces, quoted as Network Embedding, would thus be applicable to diverse predicative tasks. Numerous works exploiting pairwise proximities, one characteristic owned by real networks, the clustering property, namely vertices are inclined to form communities of various ranges and hence form a hierarchy consisting of communities, has barely received attention from researchers. In this paper, we propose our network embedding framework, abbreviated SpaceNE, preserving hierarchies formed by communities through subspaces, manifolds with flexible dimensionalities and are inherently hierarchical. Moreover, we propose that subspaces are able to address further problems in representing hierarchical communities, including sparsity and space warps. Last but not least, we proposed constraints on dimensions of subspaces to denoise, which are further approximated by differentiable functions such that joint optimization is enabled, along with a layer-wise scheme to alleviate the overhead cause by vast number of parameters. We conduct various experiments with results demonstrating our model's effectiveness in addressing community hierarchies.