TensorMode Algorithm for Network Embedding in Dynamic Environments

Network embeddings into metric spaces provide convenient representations of learned relationships between features attached to nodes and links. Embeddings into low dimensional Euclidean spaces have been successfully used for tasks such as link prediction and node classification. We consider the problem of finding effective low dimensional embeddings for dynamic networks – a family of networks indexed by a set of discrete times where there may exist both temporal and spatial links between nodes. We present novel embedding methods for a dynamic network based on higher order tensor decompositions for tensorial representations of the dynamic network. In one sense, our embeddings are analogous to spectral embedding methods for static networks. This analogy yields some mathematical intuition to help explain the effectiveness of these algorithms. Finally, we demonstrate the power and efficiency of our approach by comparing our algorithms’ performance on the link prediction task against an array of current baseline methods across three distinct real-world dynamic networks.