# Generating Post-hoc Explanations for Skip-gram-based Node Embeddings by Identifying Important Nodes with Bridgeness

arXiv: https://arxiv.org/abs/2304.12036 · HTML: https://mlsanity.com/paper/2304.12036/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 74 references that are in the map.
- First posted on arXiv 24 Apr 2023.

## Builds on (most cited first, 30 of 39)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (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)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [The (Un)reliability of saliency methods](https://mlsanity.com/paper/1711.00867/) (2017)
- [On Explainability of Graph Neural Networks via Subgraph Explorations](https://mlsanity.com/paper/2102.05152/) (2021)
- [Understanding Neural Networks through Representation Erasure](https://mlsanity.com/paper/1612.08220/) (2016)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [XGNN: Towards Model-Level Explanations of Graph Neural Networks](https://mlsanity.com/paper/2006.02587/) (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)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [Interpreting Graph Neural Networks for NLP With Differentiable Edge Masking](https://mlsanity.com/paper/2010.00577/) (2020)
- [Higher-Order Explanations of Graph Neural Networks via Relevant Walks](https://mlsanity.com/paper/2006.03589/) (2020)
- [Sanity Checks for Saliency Metrics](https://mlsanity.com/paper/1912.01451/) (2019)
- [CF-GNNExplainer: Counterfactual Explanations for Graph Neural Networks](https://mlsanity.com/paper/2102.03322/) (2021)
- [A Gentle Introduction to Deep Learning for Graphs](https://mlsanity.com/paper/1912.12693/) (2019)
- [PTE: Predictive Text Embedding through Large-scale Heterogeneous Text Networks](https://mlsanity.com/paper/1508.00200/) (2015)
- [k-hop Graph Neural Networks](https://mlsanity.com/paper/1907.06051/) (2019)
- [word2vec Parameter Learning Explained](https://mlsanity.com/paper/1411.2738/) (2014)
- [Machine Learning for Integrating Data in Biology and Medicine: Principles, Practice, and Opportunities](https://mlsanity.com/paper/1807.00123/) (2018)

## Built on by (most cited first, 4 of 4)

- [DINE: Dimensional Interpretability of Node Embeddings](https://mlsanity.com/paper/2310.01162/) (2023)
- [Federated Recommender System with Data Valuation for E-commerce Platform](https://mlsanity.com/paper/2509.11196/) (2025)
- [UNR-Explainer: Counterfactual Explanations for Unsupervised Node Representation Learning Models](https://mlsanity.com/paper/2605.17285/) (2026)
- [Semantic Prioritization in Visual Counterfactual Explanations with Weighted Segmentation and Auto-Adaptive Region Selection](https://mlsanity.com/paper/2511.12992/) (2025)

## Abstract (arXiv)

Node representation learning in a network is an important machine learning technique for encoding relational information in a continuous vector space while preserving the inherent properties and structures of the network. Recently, unsupervised node embedding methods such as DeepWalk, LINE, struc2vec, PTE, UserItem2vec, and RWJBG have emerged from the Skip-gram model and perform better performance in several downstream tasks such as node classification and link prediction than the existing relational models. However, providing post-hoc explanations of Skip-gram-based embeddings remains a challenging problem because of the lack of explanation methods and theoretical studies applicable for embeddings. In this paper, we first show that global explanations to the Skip-gram-based embeddings can be found by computing bridgeness under a spectral cluster-aware local perturbation. Moreover, a novel gradient-based explanation method, which we call GRAPH-wGD, is proposed that allows the top-q global explanations about learned graph embedding vectors more efficiently. Experiments show that the ranking of nodes by scores using GRAPH-wGD is highly correlated with true bridgeness scores. We also observe that the top-q node-level explanations selected by GRAPH-wGD have higher importance scores and produce more changes in class label prediction when perturbed, compared with the nodes selected by recent alternatives, using five real-world graphs.