# Generating Human Understandable Explanations for Node Embeddings

arXiv: https://arxiv.org/abs/2406.07642 · HTML: https://mlsanity.com/paper/2406.07642/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 56 references that are in the map.
- First posted on arXiv 11 Jun 2024.

## Builds on (most cited first, 30 of 32)

- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [On Explainability of Graph Neural Networks via Subgraph Explorations](https://mlsanity.com/paper/2102.05152/) (2021)
- [A Survey on the Explainability of Supervised Machine Learning](https://mlsanity.com/paper/2011.07876/) (2020)
- [Graph Representation Learning via Graphical Mutual Information Maximization](https://mlsanity.com/paper/2002.01169/) (2020)
- [PGM-Explainer: Probabilistic Graphical Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2010.05788/) (2020)
- [GraphLIME: Local Interpretable Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2001.06216/) (2020)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [Explainability Techniques for Graph Convolutional Networks](https://mlsanity.com/paper/1905.13686/) (2019)
- [Machine Learning on Graphs: A Model and Comprehensive Taxonomy](https://mlsanity.com/paper/2005.03675/) (2020)
- [Higher-Order Explanations of Graph Neural Networks via Relevant Walks](https://mlsanity.com/paper/2006.03589/) (2020)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Evaluating Explainability for Graph Neural Networks](https://mlsanity.com/paper/2208.09339/) (2022)
- [Analogies Explained: Towards Understanding Word Embeddings](https://mlsanity.com/paper/1901.09813/) (2019)
- [GraphSVX: Shapley Value Explanations for Graph Neural Networks](https://mlsanity.com/paper/2104.10482/) (2021)
- [Towards Understanding Linear Word Analogies](https://mlsanity.com/paper/1810.04882/) (2018)
- [RelEx: A Model-Agnostic Relational Model Explainer](https://mlsanity.com/paper/2006.00305/) (2020)
- [On the Dimensionality of Word Embedding](https://mlsanity.com/paper/1812.04224/) (2018)
- [Multi-channel Weighted Nuclear Norm Minimization for Real Color Image Denoising](https://mlsanity.com/paper/1705.09912/) (2017)
- [Stacking Models for Nearly Optimal Link Prediction in Complex Networks](https://mlsanity.com/paper/1909.07578/) (2019)
- [A Survey of Explainable Graph Neural Networks: Taxonomy and Evaluation Metrics](https://mlsanity.com/paper/2207.12599/) (2022)
- [FlowX: Towards Explainable Graph Neural Networks via Message Flows](https://mlsanity.com/paper/2206.12987/) (2022)
- [A Meta-Learning Approach for Training Explainable Graph Neural Networks](https://mlsanity.com/paper/2109.09426/) (2021)
- [Graph Neural Networks Including Sparse Interpretability](https://mlsanity.com/paper/2007.00119/) (2020)
- [Systematic comparison of graph embedding methods in practical tasks](https://mlsanity.com/paper/2106.10198/) (2021)
- [Node Proximity Is All You Need: Unified Structural and Positional Node and Graph Embedding](https://mlsanity.com/paper/2102.13582/) (2021)
- [Classic Graph Structural Features Outperform Factorization-Based Graph Embedding Methods on Community Labeling](https://mlsanity.com/paper/2201.08481/) (2022)
- [DimCL: Dimensional Contrastive Learning For Improving Self-Supervised Learning](https://mlsanity.com/paper/2309.11782/) (2023)

## Built on by (most cited first, 2 of 2)

- [Disentangled and Self-Explainable Node Representation Learning](https://mlsanity.com/paper/2410.21043/) (2024)
- [TACENR: Task-Agnostic Contrastive Explanations for Node Representations](https://mlsanity.com/paper/2604.19372/) (2026)

## Abstract (arXiv)

Node embedding algorithms produce low-dimensional latent representations of nodes in a graph. These embeddings are often used for downstream tasks, such as node classification and link prediction. In this paper, we investigate the following two questions: (Q1) Can we explain each embedding dimension with human-understandable graph features (e.g. degree, clustering coefficient and PageRank). (Q2) How can we modify existing node embedding algorithms to produce embeddings that can be easily explained by human-understandable graph features? We find that the answer to Q1 is yes and introduce a new framework called XM (short for eXplain eMbedding) to answer Q2. A key aspect of XM involves minimizing the nuclear norm of the generated explanations. We show that by minimizing the nuclear norm, we minimize the lower bound on the entropy of the generated explanations. We test XM on a variety of real-world graphs and show that XM not only preserves the performance of existing node embedding methods, but also enhances their explainability.