  Graph representation learning aims at transforming graph data into meaningful
low-dimensional vectors to facilitate the employment of machine learning and
data mining algorithms designed for general data. Most current graph
representation learning approaches are transductive, which means that they
require all the nodes in the graph are known when learning graph
representations and these approaches cannot naturally generalize to unseen
nodes. In this paper, we present a Fast Inductive Graph Representation Learning
framework (FI-GRL) to learn nodes' low-dimensional representations. Our
approach can obtain accurate representations for seen nodes with provable
theoretical guarantees and can easily generalize to unseen nodes. Specifically,
in order to explicitly decouple nodes' relations expressed by the graph, we
transform nodes into a randomized subspace spanned by a random projection
matrix. This stage is guaranteed to preserve the projection-cost of the
normalized random walk matrix which is highly related to the normalized cut of
the graph. Then feature extraction is achieved by conducting singular value
decomposition on the obtained matrix sketch. By leveraging the property of
projection-cost preservation on the matrix sketch, the obtained representation
result is nearly optimal. To deal with unseen nodes, we utilize folding-in
technique to learn their meaningful representations. Empirically, when the
amount of seen nodes are larger than that of unseen nodes, FI-GRL always
achieves excellent results. Our algorithm is fast, simple to implement and
theoretically guaranteed. Extensive experiments on real datasets demonstrate
the superiority of our algorithm on both efficacy and efficiency over both
macroscopic level (clustering) and microscopic level (structural hole
detection) applications.
