REFINE: Random RangE FInder for Network Embedding

Network embedding approaches have recently attracted considerable interest as they learn low-dimensional vector representations of nodes. Embeddings based on the matrix factorization are effective but they are usually computationally expensive due to the eigen-decomposition step. In this paper, we propose a Random RangE FInder based Network Embedding (REFINE) algorithm, which can perform embedding on one million of nodes (YouTube) within 30 seconds in a single thread. REFINE is 10x faster than ProNE, which is 10 - 400x faster than other methods such as LINE, DeepWalk, Node2Vec, GraRep, and Hope. Firstly, we formulate our network embedding approach as a skip-gram model, but with an orthogonal constraint, and we reformulate it into the matrix factorization problem. Instead of using randomized tSVD (truncated SVD) as other methods, we employ the Randomized Blocked QR decomposition to obtain the node representation fast. Moreover, we design a simple but efficient spectral filter for network enhancement to obtain higher-order information for node representation. Experimental results prove that REFINE is very efficient on datasets of different sizes (from thousand to million of nodes and edges) for node classification, while enjoying a good performance.