In graph embedding, the connectivity information of a graph is used to represent each vertex as a point in a d-dimensional space. Unlike the original, irregular structural information, such a representation can be used for a multitude of machine learning tasks. Although the process is extremely useful in practice, it is indeed expensive and unfortunately, the graphs are becoming larger and harder to embed. Attempts at scaling up the process to larger graphs have been successful but often at a steep price in hardware requirements. We present GOSH, an approach for embedding graphs of arbitrary sizes on a single GPU with minimum constraints. GOSH utilizes a novel graph coarsening approach to compress the graph and minimize the work required for embedding, delivering high-quality embeddings at a fraction of the time compared to the state-of-the-art. In addition to this, it incorporates a decomposition schema that enables any arbitrarily large graph to be embedded using a single GPU with minimum constraints on the memory size. With these techniques, GOSH is able to embed a graph with over 65 million vertices and 1.8 billion edges in less than an hour on a single GPU and obtains a 93% AUCROC for link-prediction which can be increased to 95% by running the tool for 80 minutes.
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