A Broader Picture of Random-walk Based Graph Embedding

Arlei Lopes da Silva

Abstract: Graph embedding based on random-walks supports effective so- lutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly dif- ficult to compare existing methods and to identify opportunities to advance the state-of-the-art. Meanwhile, existing work has left several fundamental questions—such as how embeddings capture different structural scales and how they should be applied for ef- fective link prediction—unanswered. This paper addresses these challenges with an analytical framework for random-walk based graph embedding that consists of three components: a random- walk process, a similarity function, and an embedding algorithm. Our framework not only categorizes many existing approaches but naturally motivates new ones. With it, we illustrate novel ways to incorporate embeddings at multiple scales to improve downstream task performance. We also show that embeddings based on autoco- variance similarity, when paired with dot product ranking for link prediction, outperform state-of-the-art methods based on Pointwise Mutual Information similarity by up to 100%.