# High-order joint embedding for multi-level link prediction

arXiv: https://arxiv.org/abs/2111.05265 · HTML: https://mlsanity.com/paper/2111.05265/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 50 references that are in the map.
- First posted on arXiv 7 Nov 2021.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [Random Walks on Hypergraphs with Edge-Dependent Vertex Weights](https://mlsanity.com/paper/1905.08287/) (2019)
- [Estimating network edge probabilities by neighborhood smoothing](https://mlsanity.com/paper/1509.08588/) (2015)
- [Evolutionary dynamics of higher-order interactions in social networks](https://mlsanity.com/paper/2001.10313/) (2020)
- [Link prediction for partially observed networks](https://mlsanity.com/paper/1301.7047/) (2013)
- [A Multilayer Approach to Multiplexity and Link Prediction in Online Geo-Social Networks](https://mlsanity.com/paper/1508.07876/) (2015)

## Built on by (most cited first, 1 of 1)

- [NetworkNet: A Deep Neural Network Approach for Random Networks with Sparse Nodal Attributes and Complex Nodal Heterogeneity](https://mlsanity.com/paper/2604.11673/) (2026)

## Abstract (arXiv)

Link prediction infers potential links from observed networks, and is one of the essential problems in network analyses. In contrast to traditional graph representation modeling which only predicts two-way pairwise relations, we propose a novel tensor-based joint network embedding approach on simultaneously encoding pairwise links and hyperlinks onto a latent space, which captures the dependency between pairwise and multi-way links in inferring potential unobserved hyperlinks. The major advantage of the proposed embedding procedure is that it incorporates both the pairwise relationships and subgroup-wise structure among nodes to capture richer network information. In addition, the proposed method introduces a hierarchical dependency among links to infer potential hyperlinks, and leads to better link prediction. In theory we establish the estimation consistency for the proposed embedding approach, and provide a faster convergence rate compared to link prediction utilizing pairwise links or hyperlinks only. Numerical studies on both simulation settings and Facebook ego-networks indicate that the proposed method improves both hyperlink and pairwise link prediction accuracy compared to existing link prediction algorithms.