A flexible PageRank-based graph embedding framework closely related to spectral eigenvector embeddings
This provides a general embedding strategy for applications where spectral techniques are not well-established, such as hypergraphs, but it is incremental as it builds on existing PageRank methods.
The authors tackled the problem of graph embedding by proposing a flexible framework based on personalized PageRank vectors, showing it relates to spectral embeddings for certain graphs and enables local representations with a relatively small number of vectors.
We study a simple embedding technique based on a matrix of personalized PageRank vectors seeded on a random set of nodes. We show that the embedding produced by the element-wise logarithm of this matrix (1) are related to the spectral embedding for a class of graphs where spectral embeddings are significant, and hence useful representation of the data, (2) can be done for the entire network or a smaller part of it, which enables precise local representation, and (3) uses a relatively small number of PageRank vectors compared to the size of the networks. Most importantly, the general nature of this embedding strategy opens up many emerging applications, where eigenvector and spectral techniques may not be well established, to the PageRank-based relatives. For instance, similar techniques can be used on PageRank vectors from hypergraphs to get "spectral-like" embeddings.