mlsanityData to 7 Oct 2026

Contrastive Laplacian Eigenmaps

arXiv 2201.05493 ↗First posted 14 Jan 2022cs.LGcited by 24

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Abstract (arXiv)

Graph contrastive learning attracts/disperses node representations for similar/dissimilar node pairs under some notion of similarity. It may be combined with a low-dimensional embedding of nodes to preserve intrinsic and structural properties of a graph. In this paper, we extend the celebrated Laplacian Eigenmaps with contrastive learning, and call them COntrastive Laplacian EigenmapS (COLES). Starting from a GAN-inspired contrastive formulation, we show that the Jensen-Shannon divergence underlying many contrastive graph embedding models fails under disjoint positive and negative distributions, which may naturally emerge during sampling in the contrastive setting. In contrast, we demonstrate analytically that COLES essentially minimizes a surrogate of Wasserstein distance, which is known to cope well under disjoint distributions. Moreover, we show that the loss of COLES belongs to the family of so-called block-contrastive losses, previously shown to be superior compared to pair-wise losses typically used by contrastive methods. We show on popular benchmarks/backbones that COLES offers favourable accuracy/scalability compared to DeepWalk, GCN, Graph2Gauss, DGI and GRACE baselines.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 43 of its 65 references that are in the map. First posted on arXiv 14 Jan 2022.

Builds on

43 of 65 references.

References · 43

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31 more
  1. 2020Graph Contrastive Learning with Augmentationscited by 1,203
  2. 2018Deep Graph Infomaxcited by 1,101
  3. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,099
  4. 2018Pitfalls of Graph Neural Network Evaluationcited by 994
  5. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  6. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 970
  7. 2019Learning Representations by Maximizing Mutual Information Across Viewscited by 733
  8. 2020Contrastive Multi-View Representation Learning on Graphscited by 651
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  10. 2015LINE: Large-scale Information Network Embeddingcited by 582
  11. 2020Deep Graph Contrastive Representation Learningcited by 535
  12. 2019A Theoretical Analysis of Contrastive Unsupervised Representation Learningcited by 530
  13. 2020Graph Contrastive Learning with Adaptive Augmentationcited by 519
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  25. 2021How Framelets Enhance Graph Neural Networkscited by 46
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Cited by year

Citing papers per year: 2022: 8; 2023: 10; 2024: 5; 2025: 1.

24 papers.

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  1. 2022Spectral Feature Augmentation for Graph Contrastive Learning and Beyondcited by 49
  2. 20233Mformer: Multi-order Multi-mode Transformer for Skeletal Action Recognitioncited by 40
  3. 2022COSTA: Covariance-Preserving Feature Augmentation for Graph Contrastive Learningcited by 38
  4. 2023Simple and Asymmetric Graph Contrastive Learning without Augmentationscited by 37
  5. 2022Temporal-Viewpoint Transportation Plan for Skeletal Few-shot Action Recognitioncited by 22
  6. 2022Uncertainty-DTW for Time Series and Sequencescited by 21
  7. 2022SCGC : Self-Supervised Contrastive Graph Clusteringcited by 13
  8. 2022Graph-adaptive Rectified Linear Unit for Graph Neural Networkscited by 12
  9. 2023Traffic Forecasting on New Roads Using Spatial Contrastive Pre-Training (SCPT)cited by 11
  10. 2023Pre-training with Random Orthogonal Projection Image Modelingcited by 11
  11. 2022MA-GCL: Model Augmentation Tricks for Graph Contrastive Learningcited by 10
  12. 2024Meet JEANIE: a Similarity Measure for 3D Skeleton Sequences via Temporal-Viewpoint Alignmentcited by 10
12 more
  1. 2023Because Every Sensor Is Unique, so Is Every Pair: Handling Dynamicity in Traffic Forecastingcited by 9
  2. 2023Understanding and Mitigating Hyperbolic Dimensional Collapse in Graph Contrastive Learningcited by 9
  3. 2024A Survey on Self-Supervised Graph Foundation Models: Knowledge-Based Perspectivecited by 9
  4. 2024Cluster Aware Graph Anomaly Detectioncited by 7
  5. 2023The Galerkin method beats Graph-Based Approaches for Spectral Algorithmscited by 6
  6. 2023Self-Contrastive Graph Diffusion Networkcited by 4
  7. 2023A Contrastive Variational Graph Auto-Encoder for Node Clusteringcited by 4
  8. 2022Efficient block contrastive learning via parameter-free meta-node approximationcited by 2
  9. 2023StructComp: Substituting Propagation with Structural Compression in Training Graph Contrastive Learningcited by 2
  10. 2025Graph Self-Supervised Learning with Learnable Structural and Positional Encodingscited by 1
  11. 2024Your Graph Recommender is Provably a Single-view Graph Contrastive Learningcited by 0
  12. 2024GNN-Transformer Cooperative Architecture for Trustworthy Graph Contrastive Learningcited by 0