  Network embedding aims to learn low-dimensional representations of nodes in a
network, while the network structure and inherent properties are preserved. It
has attracted tremendous attention recently due to significant progress in
downstream network learning tasks, such as node classification, link
prediction, and visualization. However, most existing network embedding methods
suffer from the expensive computations due to the large volume of networks. In
this paper, we propose a $10\times \sim 100\times$ faster network embedding
method, called Progle, by elegantly utilizing the sparsity property of online
networks and spectral analysis. In Progle, we first construct a \textit{sparse}
proximity matrix and train the network embedding efficiently via sparse matrix
decomposition. Then we introduce a network propagation pattern via spectral
analysis to incorporate local and global structure information into the
embedding. Besides, this model can be generalized to integrate network
information into other insufficiently trained embeddings at speed. Benefiting
from sparse spectral network embedding, our experiment on four different
datasets shows that Progle outperforms or is comparable to state-of-the-art
unsupervised comparison approaches---DeepWalk, LINE, node2vec, GraRep, and
HOPE, regarding accuracy, while is $10\times$ faster than the fastest
word2vec-based method. Finally, we validate the scalability of Progle both in
real large-scale networks and multiple scales of synthetic networks.
