# SpeGCL: Self-supervised Graph Spectrum Contrastive Learning without Positive Samples

arXiv: https://arxiv.org/abs/2410.10365 · HTML: https://mlsanity.com/paper/2410.10365/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 67 of its 99 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## Builds on (most cited first, 30 of 67)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [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)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [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)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [GCC: Graph Contrastive Coding for Graph Neural Network Pre-Training](https://mlsanity.com/paper/2006.09963/) (2020)
- [GraphMAE: Self-Supervised Masked Graph Autoencoders](https://mlsanity.com/paper/2205.10803/) (2022)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [High Frequency Component Helps Explain the Generalization of Convolutional Neural Networks](https://mlsanity.com/paper/1905.13545/) (2019)
- [GPT-GNN: Generative Pre-Training of Graph Neural Networks](https://mlsanity.com/paper/2006.15437/) (2020)
- [A Fourier Perspective on Model Robustness in Computer Vision](https://mlsanity.com/paper/1906.08988/) (2019)
- [Graph Contrastive Learning Automated](https://mlsanity.com/paper/2106.07594/) (2021)
- [graph2vec: Learning Distributed Representations of Graphs](https://mlsanity.com/paper/1707.05005/) (2017)
- [Adversarial Graph Augmentation to Improve Graph Contrastive Learning](https://mlsanity.com/paper/2106.05819/) (2021)

## Built on by (most cited first, 20 of 20)

- [Graph Domain Adaptation with Dual-branch Encoder and Two-level Alignment for Whole Slide Image-based Survival Prediction](https://mlsanity.com/paper/2411.14001/) (2024)
- [MCSFF: Multi-modal Consistency and Specificity Fusion Framework for Entity Alignment](https://mlsanity.com/paper/2410.14584/) (2024)
- [Graph Contrastive Learning via Cluster-refined Negative Sampling for Semi-supervised Text Classification](https://mlsanity.com/paper/2410.18130/) (2024)
- [The Paradigm Shift: A Comprehensive Survey on Large Vision Language Models for Multimodal Fake News Detection](https://mlsanity.com/paper/2601.15316/) (2026)
- [Contrastive Multi-graph Learning with Neighbor Hierarchical Sifting for Semi-supervised Text Classification](https://mlsanity.com/paper/2411.16787/) (2024)
- [Dynamic Graph Neural ODE Network for Multi-modal Emotion Recognition in Conversation](https://mlsanity.com/paper/2412.02935/) (2024)
- [GroupFace: Imbalanced Age Estimation Based on Multi-hop Attention Graph Convolutional Network and Group-aware Margin Optimization](https://mlsanity.com/paper/2412.11450/) (2024)
- [Dual-branch Graph Domain Adaptation for Cross-scenario Multi-modal Emotion Recognition](https://mlsanity.com/paper/2603.26840/) (2026)
- [SE-GCL: An Event-Based Simple and Effective Graph Contrastive Learning for Text Representation](https://mlsanity.com/paper/2412.11652/) (2024)
- [LRA-GNN: Latent Relation-Aware Graph Neural Network with Initial and Dynamic Residual for Facial Age Estimation](https://mlsanity.com/paper/2502.05423/) (2025)
- [A Flow Model with Low-Rank Transformers for Incomplete Multimodal Survival Analysis](https://mlsanity.com/paper/2510.21829/) (2025)
- [SE-GNN: Seed Expanded-Aware Graph Neural Network with Iterative Optimization for Semi-supervised Entity Alignment](https://mlsanity.com/paper/2503.20801/) (2025)
- [GSDNet: Revisiting Incomplete Multimodal-Diffusion from Graph Spectrum Perspective for Conversation Emotion Recognition](https://mlsanity.com/paper/2506.12325/) (2025)
- [Attention Beyond Neighborhoods: Reviving Transformer for Graph Clustering](https://mlsanity.com/paper/2509.15024/) (2025)
- [TimeGNN-Augmented Hybrid-Action MARL for Fine-Grained Task Partitioning and Energy-Aware Offloading in MEC](https://mlsanity.com/paper/2601.06191/) (2026)
- [AMB-DSGDN: Adaptive Modality-Balanced Dynamic Semantic Graph Differential Network for Multimodal Emotion Recognition](https://mlsanity.com/paper/2603.10043/) (2026)
- [Dynamic Fusion-Aware Graph Convolutional Neural Network for Multimodal Emotion Recognition in Conversations](https://mlsanity.com/paper/2603.22345/) (2026)
- [Relational graph-driven differential denoising and diffusion attention fusion for multimodal conversation emotion recognition](https://mlsanity.com/paper/2603.25752/) (2026)
- [Disentangled Dual-Branch Graph Learning for Conversational Emotion Recognition](https://mlsanity.com/paper/2604.14204/) (2026)
- [C2MOE: Consistency and Complementarity-guided Mixture of Experts for Incomplete Multimodal Emotion Learning](https://mlsanity.com/paper/2608.04013/) (2026)

## Abstract (arXiv)

Graph Contrastive Learning (GCL) excels at managing noise and fluctuations in input data, making it popular in various fields (e.g., social networks, and knowledge graphs). Our study finds that the difference in high-frequency information between augmented graphs is greater than that in low-frequency information. However, most existing GCL methods focus mainly on the time domain (low-frequency information) for node feature representations and cannot make good use of high-frequency information to speed up model convergence. Furthermore, existing GCL paradigms optimize graph embedding representations by pulling the distance between positive sample pairs closer and pushing the distance between positive and negative sample pairs farther away, but our theoretical analysis shows that graph contrastive learning benefits from pushing negative pairs farther away rather than pulling positive pairs closer. To solve the above-mentioned problems, we propose a novel spectral GCL framework without positive samples, named SpeGCL. Specifically, to solve the problem that existing GCL methods cannot utilize high-frequency information, SpeGCL uses a Fourier transform to extract high-frequency and low-frequency information of node features, and constructs a contrastive learning mechanism in a Fourier space to obtain better node feature representation. Furthermore, SpeGCL relies entirely on negative samples to refine the graph embedding. We also provide a theoretical justification for the efficacy of using only negative samples in SpeGCL. Extensive experiments on un-supervised learning, transfer learning, and semi-supervised learning have validated the superiority of our SpeGCL framework over the state-of-the-art GCL methods.