# Graph Embedding with Hierarchical Attentive Membership

arXiv: https://arxiv.org/abs/2111.00604 · HTML: https://mlsanity.com/paper/2111.00604/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 48 references that are in the map.
- First posted on arXiv 31 Oct 2021.

## Builds on (most cited first, 25 of 25)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [HARP: Hierarchical Representation Learning for Networks](https://mlsanity.com/paper/1706.07845/) (2017)
- [Semi-Supervised Graph Classification: A Hierarchical Graph Perspective](https://mlsanity.com/paper/1904.05003/) (2019)
- [Hierarchical Block Structures and High-resolution Model Selection in Large Networks](https://mlsanity.com/paper/1310.4377/) (2013)
- [Link Prediction with Persistent Homology: An Interactive View](https://mlsanity.com/paper/2102.10255/) (2021)
- [Is a Single Vector Enough? Exploring Node Polysemy for Network Embedding](https://mlsanity.com/paper/1905.10668/) (2019)
- [Is a Single Embedding Enough? Learning Node Representations that Capture Multiple Social Contexts](https://mlsanity.com/paper/1905.02138/) (2019)
- [Graph Structural-topic Neural Network](https://mlsanity.com/paper/2006.14278/) (2020)
- [Unsupervised Differentiable Multi-aspect Network Embedding](https://mlsanity.com/paper/2006.04239/) (2020)
- [Collective Link Prediction Oriented Network Embedding with Hierarchical Graph Attention](https://mlsanity.com/paper/1910.05736/) (2019)
- [Consistency of Spectral Clustering on Hierarchical Stochastic Block Models](https://mlsanity.com/paper/2004.14531/) (2020)
- [JNET: Learning User Representations via Joint Network Embedding and Topic Embedding](https://mlsanity.com/paper/1912.00465/) (2019)

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

- [A Contextual Master-Slave Framework on Urban Region Graph for Urban Village Detection](https://mlsanity.com/paper/2211.14633/) (2022)
- [Globally Interpretable Graph Learning via Distribution Matching](https://mlsanity.com/paper/2306.10447/) (2023)
- [KAA: Kolmogorov-Arnold Attention for Enhancing Attentive Graph Neural Networks](https://mlsanity.com/paper/2501.13456/) (2025)
- [Attention-based graph neural networks: a survey](https://mlsanity.com/paper/2605.08679/) (2026)

## Abstract (arXiv)

The exploitation of graph structures is the key to effectively learning representations of nodes that preserve useful information in graphs. A remarkable property of graph is that a latent hierarchical grouping of nodes exists in a global perspective, where each node manifests its membership to a specific group based on the context composed by its neighboring nodes. Most prior works ignore such latent groups and nodes' membership to different groups, not to mention the hierarchy, when modeling the neighborhood structure. Thus, they fall short of delivering a comprehensive understanding of the nodes under different contexts in a graph. In this paper, we propose a novel hierarchical attentive membership model for graph embedding, where the latent memberships for each node are dynamically discovered based on its neighboring context. Both group-level and individual-level attentions are performed when aggregating neighboring states to generate node embeddings. We introduce structural constraints to explicitly regularize the inferred memberships of each node, such that a well-defined hierarchical grouping structure is captured. The proposed model outperformed a set of state-of-the-art graph embedding solutions on node classification and link prediction tasks in a variety of graphs including citation networks and social networks. Qualitative evaluations visualize the learned node embeddings along with the inferred memberships, which proved the concept of membership hierarchy and enables explainable embedding learning in graphs.