Towards Understanding the Instability of Network Embedding

Network embedding algorithms learn a mapping from the discrete representation of nodes to continuous vector spaces that preserve the proximities of nodes. The techniques have a wide range of applications in various downstream tasks such as node classification, link prediction, and network alignment. Despite recent efforts to the design of novel models, little attention has been paid to understanding the instability of network embedding. In this paper, we fill this gap by investigating several state-of-the-art network embedding methods. Node embeddings form a geometric shape in the latent space. Characterizing the geometry is critical to figure out the variance of network embedding. Hence, we define two metrics to characterize the geometric properties and find that node embeddings tremble in different instantiations of an embedding space. Then, we formally define the stability of node embeddings as the invariance of the nearest neighbors of nodes. Experimental results show that existing embedding approaches have significant amounts of instability. We explore the influence factors that affect the stability of different methods and find that both network structure and algorithm models affect the stability of node embeddings significantly. Finally, we examine the implications of embedding instability for downstream tasks and find remarkable impacts on the performance.