  Newly arriving nodes in dynamics networks would gradually make the node
embedding space drifted and the retraining of node embedding and downstream
models indispensable. An exact threshold size of these new nodes, below which
the node embedding space will be predicatively maintained, however, is rarely
considered in either theory or experiment. From the view of matrix perturbation
theory, a threshold of the maximum number of new nodes that keep the node
embedding space approximately equivalent is analytically provided and
empirically validated. It is therefore theoretically guaranteed that as the
size of newly arriving nodes is below this threshold, embeddings of these new
nodes can be quickly derived from embeddings of original nodes. A generation
framework, Space-Invariant Projection (SIP), is accordingly proposed to enables
arbitrary static MF-based embedding schemes to embed new nodes in dynamics
networks fast. The time complexity of SIP is linear with the network size. By
combining SIP with four state-of-the-art MF-based schemes, we show that SIP
exhibits not only wide adaptability but also strong empirical performance in
terms of efficiency and efficacy on the node classification task in three real
datasets.
