# Efficient Identity and Position Graph Embedding via Spectral-Based Random Feature Aggregation

arXiv: https://arxiv.org/abs/2505.20992 · HTML: https://mlsanity.com/paper/2505.20992/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 66 references that are in the map.
- First posted on arXiv 27 May 2025.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [GraphMAE: Self-Supervised Masked Graph Autoencoders](https://mlsanity.com/paper/2205.10803/) (2022)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [Identity-aware Graph Neural Networks](https://mlsanity.com/paper/2101.10320/) (2021)
- [GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learner](https://mlsanity.com/paper/2304.04779/) (2023)
- [AM-GCN: Adaptive Multi-channel Graph Convolutional Networks](https://mlsanity.com/paper/2007.02265/) (2020)
- [Learning Structural Node Embeddings Via Diffusion Wavelets](https://mlsanity.com/paper/1710.10321/) (2017)
- [Rethinking and Scaling Up Graph Contrastive Learning: An Extremely Efficient Approach with Group Discrimination](https://mlsanity.com/paper/2206.01535/) (2022)
- [Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning](https://mlsanity.com/paper/2007.16002/) (2020)
- [NetSMF: Large-Scale Network Embedding as Sparse Matrix Factorization](https://mlsanity.com/paper/1906.11156/) (2019)
- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [AdaGNN: Graph Neural Networks with Adaptive Frequency Response Filter](https://mlsanity.com/paper/2104.12840/) (2021)
- [Structure and inference in annotated networks](https://mlsanity.com/paper/1507.04001/) (2015)
- [Billion-scale Network Embedding with Iterative Random Projection](https://mlsanity.com/paper/1805.02396/) (2018)
- [GraLSP: Graph Neural Networks with Local Structural Patterns](https://mlsanity.com/paper/1911.07675/) (2019)
- [20 years of network community detection](https://mlsanity.com/paper/2208.00111/) (2022)
- [Temporal Link Prediction: A Unified Framework, Taxonomy, and Review](https://mlsanity.com/paper/2210.08765/) (2022)
- [Node Proximity Is All You Need: Unified Structural and Positional Node and Graph Embedding](https://mlsanity.com/paper/2102.13582/) (2021)
- [CSGCL: Community-Strength-Enhanced Graph Contrastive Learning](https://mlsanity.com/paper/2305.04658/) (2023)
- [Improvements on SCORE, Especially for Weak Signals](https://mlsanity.com/paper/1811.05927/) (2018)
- [Discovering Representative Attribute-stars via Minimum Description Length](https://mlsanity.com/paper/2204.12704/) (2022)
- [Pre-train and Refine: Towards Higher Efficiency in K-Agnostic Community Detection without Quality Degradation](https://mlsanity.com/paper/2405.20277/) (2024)
- [A Survey on Role-Oriented Network Embedding](https://mlsanity.com/paper/2107.08379/) (2021)
- [ProCom: A Few-shot Targeted Community Detection Algorithm](https://mlsanity.com/paper/2408.07369/) (2024)

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

- [InfraredGP: Efficient Graph Partitioning via Spectral Graph Neural Networks with Negative Corrections](https://mlsanity.com/paper/2508.19737/) (2025)
- [Topology-induced Operators Reveal Complementary Graph Representations without Training](https://mlsanity.com/paper/2609.08152/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs), which capture graph structures via a feature aggregation mechanism following the graph embedding framework, have demonstrated a powerful ability to support various tasks. According to the topology properties (e.g., structural roles or community memberships of nodes) to be preserved, graph embedding can be categorized into identity and position embedding. However, it is unclear for most GNN-based methods which property they can capture. Some of them may also suffer from low efficiency and scalability caused by several time- and space-consuming procedures (e.g., feature extraction and training). From a perspective of graph signal processing, we find that high- and low-frequency information in the graph spectral domain may characterize node identities and positions, respectively. Based on this investigation, we propose random feature aggregation (RFA) for efficient identity and position embedding, serving as an extreme ablation study regarding GNN feature aggregation. RFA (i) adopts a spectral-based GNN without learnable parameters as its backbone, (ii) only uses random noises as inputs, and (iii) derives embeddings via just one feed-forward propagation (FFP). Inspired by degree-corrected spectral clustering, we further introduce a degree correction mechanism to the GNN backbone. Surprisingly, our experiments demonstrate that two variants of RFA with high- and low-pass filters can respectively derive informative identity and position embeddings via just one FFP (i.e., without any training). As a result, RFA can achieve a better trade-off between quality and efficiency for both identity and position embedding over various baselines.