# Conditional Network Embeddings

arXiv: https://arxiv.org/abs/1805.07544 · HTML: https://mlsanity.com/paper/1805.07544/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2018.

## Built on by (most cited first, 15 of 15)

- [FairDrop: Biased Edge Dropout for Enhancing Fairness in Graph Representation Learning](https://mlsanity.com/paper/2104.14210/) (2021)
- [Representation Bias in Data: A Survey on Identification and Resolution Techniques](https://mlsanity.com/paper/2203.11852/) (2022)
- [Unbiased Graph Embedding with Biased Graph Observations](https://mlsanity.com/paper/2110.13957/) (2021)
- [On Generalized Degree Fairness in Graph Neural Networks](https://mlsanity.com/paper/2302.03881/) (2023)
- [RawlsGCN: Towards Rawlsian Difference Principle on Graph Convolutional Network](https://mlsanity.com/paper/2202.13547/) (2022)
- [A Survey on Fairness for Machine Learning on Graphs](https://mlsanity.com/paper/2205.05396/) (2022)
- [The KL-Divergence between a Graph Model and its Fair I-Projection as a Fairness Regularizer](https://mlsanity.com/paper/2103.01846/) (2021)
- [EqGNN: Equalized Node Opportunity in Graphs](https://mlsanity.com/paper/2108.08800/) (2021)
- [Gaussian Embedding of Temporal Networks](https://mlsanity.com/paper/2405.17253/) (2024)
- [Consumer-side Fairness in Recommender Systems: A Systematic Survey of Methods and Evaluation](https://mlsanity.com/paper/2305.09330/) (2023)
- [Adversarial Robustness of Probabilistic Network Embedding for Link Prediction](https://mlsanity.com/paper/2107.01936/) (2021)
- [A Systematic Evaluation of Node Embedding Robustness](https://mlsanity.com/paper/2209.08064/) (2022)
- [FEIR: Quantifying and Reducing Envy and Inferiority for Fair Recommendation of Limited Resources](https://mlsanity.com/paper/2311.04542/) (2023)
- [How Predicted Links Influence Network Evolution: Disentangling Choice and Algorithmic Feedback in Dynamic Graphs](https://mlsanity.com/paper/2603.03945/) (2026)
- [Fairness-Aware Network Embeddings: Methods, Applications, and Challenges](https://mlsanity.com/paper/2608.19381/) (2026)

## Abstract (arXiv)

Network Embeddings (NEs) map the nodes of a given network into d-dimensional Euclidean space ℝd. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such as link prediction (if `similar' means being `more likely to be connected') or classification (if `similar' means `being more likely to have the same label'). In recent years various methods for NE have been introduced, all following a similar strategy: defining a notion of similarity between nodes (typically some distance measure within the network), a distance measure in the embedding space, and a loss function that penalizes large distances for similar nodes and small distances for dissimilar nodes. A difficulty faced by existing methods is that certain networks are fundamentally hard to embed due to their structural properties: (approximate) multipartiteness, certain degree distributions, assortativity, etc. To overcome this, we introduce a conceptual innovation to the NE literature and propose to create Conditional Network Embeddings (CNEs); embeddings that maximally add information with respect to given structural properties (e.g. node degrees, block densities, etc.). We use a simple Bayesian approach to achieve this, and propose a block stochastic gradient descent algorithm for fitting it efficiently. We demonstrate that CNEs are superior for link prediction and multi-label classification when compared to state-of-the-art methods, and this without adding significant mathematical or computational complexity. Finally, we illustrate the potential of CNE for network visualization.