# A flexible PageRank-based graph embedding framework closely related to spectral eigenvector embeddings

arXiv: https://arxiv.org/abs/2207.11321 · HTML: https://mlsanity.com/paper/2207.11321/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 69 references that are in the map.
- First posted on arXiv 22 Jul 2022.

## Builds on (most cited first, 28 of 28)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [Unifying Graph Convolutional Neural Networks and Label Propagation](https://mlsanity.com/paper/2002.06755/) (2020)
- [Learning Structural Node Embeddings Via Diffusion Wavelets](https://mlsanity.com/paper/1710.10321/) (2017)
- [PTE: Predictive Text Embedding through Large-scale Heterogeneous Text Networks](https://mlsanity.com/paper/1508.00200/) (2015)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [NetLSD: Hearing the Shape of a Graph](https://mlsanity.com/paper/1805.10712/) (2018)
- [PageRank beyond the Web](https://mlsanity.com/paper/1407.5107/) (2014)
- [Clustering in graphs and hypergraphs with categorical edge labels](https://mlsanity.com/paper/1910.09943/) (2019)
- [Heat kernel based community detection](https://mlsanity.com/paper/1403.3148/) (2014)
- [Homogeneous Network Embedding for Massive Graphs via Reweighted Personalized PageRank](https://mlsanity.com/paper/1906.06826/) (2019)
- [Nonlinear Higher-Order Label Spreading](https://mlsanity.com/paper/2006.04762/) (2020)
- [InfiniteWalk: Deep Network Embeddings as Laplacian Embeddings with a Nonlinearity](https://mlsanity.com/paper/2006.00094/) (2020)
- [Random walks on hypergraphs](https://mlsanity.com/paper/1911.06523/) (2019)
- [Scalable Graph Embeddings via Sparse Transpose Proximities](https://mlsanity.com/paper/1905.07245/) (2019)
- [Hypergraph Clustering Based on PageRank](https://mlsanity.com/paper/2006.08302/) (2020)
- [FREDE: Anytime Graph Embeddings](https://mlsanity.com/paper/2006.04746/) (2020)
- [Strongly Local Hypergraph Diffusions for Clustering and Semi-supervised Learning](https://mlsanity.com/paper/2011.07752/) (2020)
- [A nonlinear diffusion method for semi-supervised learning on hypergraphs](https://mlsanity.com/paper/2103.14867/) (2021)
- [InstantEmbedding: Efficient Local Node Representations](https://mlsanity.com/paper/2010.06992/) (2020)
- [Node and Edge Nonlinear Eigenvector Centrality for Hypergraphs](https://mlsanity.com/paper/2101.06215/) (2021)
- [AptRank: An Adaptive PageRank Model for Protein Function Prediction on Bi-relational Graphs](https://mlsanity.com/paper/1601.05506/) (2016)
- [Flow-based Algorithms for Improving Clusters: A Unifying Framework, Software, and Performance](https://mlsanity.com/paper/2004.09608/) (2020)
- [An Efficient Multilinear Optimization Framework for Hypergraph Matching](https://mlsanity.com/paper/1511.02667/) (2015)

## Abstract (arXiv)

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.