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The computation of distance measures between nodes in graphs is inefficientand does not scale to large graphs. We explore dense vector representations asan effective way to approximate the same information: we introduce a simple yetefficient and effective approach for learning graph embeddings. Instead ofdirectly operating on the graph structure, our method takes structural measuresof pairwise node similarities into account and learns dense noderepresentations reflecting user-defined graph distance measures, such ase.g.the shortest path distance or distance measures that take informationbeyond the graph structure into account. We demonstrate a speed-up of severalorders of magnitude when predicting word similarity by vector operations on ourembeddings as opposed to directly computing the respective path-based measures,while outperforming various other graph embeddings on semantic similarity andword sense disambiguation tasks and show evaluations on the WordNet graph andtwo knowledge base graphs.

Making Fast Graph-based Algorithms with Graph Metric Embeddings