# Refined Graph Encoder Embedding via Self-Training and Latent Community Recovery

arXiv: https://arxiv.org/abs/2405.12797 · HTML: https://mlsanity.com/paper/2405.12797/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 60 references that are in the map.
- First posted on arXiv 21 May 2024.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Models](https://mlsanity.com/paper/2005.07959/) (2020)
- [Statistical inference on random dot product graphs: a survey](https://mlsanity.com/paper/1709.05454/) (2017)
- [A statistical interpretation of spectral embedding: the generalised random dot product graph](https://mlsanity.com/paper/1709.05506/) (2017)
- [Inference for multiple heterogeneous networks with a common invariant subspace](https://mlsanity.com/paper/1906.10026/) (2019)
- [Graph Positional Encoding via Random Feature Propagation](https://mlsanity.com/paper/2303.02918/) (2023)
- [On a 'Two Truths' Phenomenon in Spectral Graph Clustering](https://mlsanity.com/paper/1808.07801/) (2018)
- [One-Hot Graph Encoder Embedding](https://mlsanity.com/paper/2109.13098/) (2021)
- [GraSPy: Graph Statistics in Python](https://mlsanity.com/paper/1904.05329/) (2019)
- [Spectral embedding for dynamic networks with stability guarantees](https://mlsanity.com/paper/2106.01282/) (2021)
- [Spectral embedding of weighted graphs](https://mlsanity.com/paper/1910.05534/) (2019)
- [Graph Encoder Ensemble for Simultaneous Vertex Embedding and Community Detection](https://mlsanity.com/paper/2301.11290/) (2023)
- [Generalized Canonical Correlation Analysis for Classification](https://mlsanity.com/paper/1304.7981/) (2013)
- [Simulating and Modeling the Risk of Conversational Search](https://mlsanity.com/paper/2201.00235/) (2022)
- [Synergistic Graph Fusion via Encoder Embedding](https://mlsanity.com/paper/2303.18051/) (2023)
- [Discovering Communication Pattern Shifts in Large-Scale Labeled Networks using Encoder Embedding and Vertex Dynamics](https://mlsanity.com/paper/2305.02381/) (2023)
- [Community Correlations and Testing Independence Between Binary Graphs](https://mlsanity.com/paper/1906.03661/) (2019)
- [On spectral algorithms for community detection in stochastic blockmodel graphs with vertex covariates](https://mlsanity.com/paper/2007.02156/) (2020)
- [Vertex nomination between graphs via spectral embedding and quadratic programming](https://mlsanity.com/paper/2010.14622/) (2020)

## Built on by (most cited first, 5 of 5)

- [Encoder Embedding for General Graph and Node Classification](https://mlsanity.com/paper/2405.15473/) (2024)
- [Principal Graph Encoder Embedding and Principal Community Detection](https://mlsanity.com/paper/2501.14939/) (2025)
- [A Graph Sufficiency Perspective for Neural Networks](https://mlsanity.com/paper/2507.10215/) (2025)
- [Fast and Scalable Multi-Kernel Encoder Classifier](https://mlsanity.com/paper/2406.02189/) (2024)
- [Graph Neural Networks Powered by Encoder Embedding for Improved Node Learning](https://mlsanity.com/paper/2507.11732/) (2025)

## Abstract (arXiv)

This paper introduces a refined graph encoder embedding method, enhancing the original graph encoder embedding through linear transformation, self-training, and hidden community recovery within observed communities. We provide the theoretical rationale for the refinement procedure, demonstrating how and why our proposed method can effectively identify useful hidden communities under stochastic block models. Furthermore, we show how the refinement method leads to improved vertex embedding and better decision boundaries for subsequent vertex classification. The efficacy of our approach is validated through numerical experiments, which exhibit clear advantages in identifying meaningful latent communities and improved vertex classification across a collection of simulated and real-world graph data.