Just as we did earlier when comparing similarity between colors using the dot product of their vector representation, we can measure embedded node similarity by computing the dot product of their vectors. However, we can also measure node similarity using other heuristics, like the ones we studied in Chapter 7, Community Detection and Similarity Measures. Jaccard or Adamic-Adar similarities are well-known examples of node similarity measures.
We can build a node embedding by trying to make the vector similarity of two nodes as close as possible. The node similarity in the vector space is measured by the dot product of the embedding vectors, Vi . Vj, while the node similarity in the graph is measured by a scoring function, Sij. This scoring function can be computed using any similarity measure (for instance Adamic-Adar). Reducing the difference between these two measures requires the following function to be minimized:
Φ...
