Graph Laplacian

The graph Laplacian is a matrix representation of a graph's structure, used to analyze connectivity and diffusion processes within networks. Current research focuses on extending its applications beyond traditional graph analysis, including developing parameterized Laplacians for improved performance in graph neural networks (GNNs), particularly on heterophilic graphs, and using it for tasks like image denoising, semi-supervised learning, and dimensionality reduction. These advancements improve the efficiency and accuracy of GNNs and other machine learning models, impacting fields such as signal processing, computer vision, and network analysis. Furthermore, research explores connections between the graph Laplacian and other mathematical concepts, such as optimal transport, to enhance theoretical understanding and practical applications.

Papers

October 30, 2024

Improved convergence rate of kNN graph Laplacians
Yixuan Tan, Xiuyuan Cheng
Convergence Rate Graph Laplacian Affinity Graph K$ Distance NN Graph

October 9, 2024

DLGNet: Hyperedge Classification through Directed Line Graphs for Chemical Reactions
Stefano Fiorini, Giulia M. Bovolenta, Stefano Coniglio, Michele Ciavotta, Pietro Morerio, Michele Parrinello, Alessio Del Bue
Directed Graph Graph Laplacian Spectral Graph Neural Network Hyperedge Prediction Reaction Prediction Chemical Reaction Reaction Template

September 15, 2024

Flexible Diffusion Scopes with Parameterized Laplacian for Heterophilic Graph Learning
Qincheng Lu, Jiaqi Zhu, Sitao Luan, Xiao-Wen Chang
Graph Neural Network Graph Learning Graph Attention Network Graph Laplacian

September 12, 2024

Efficient Learning of Balanced Signed Graphs via Iterative Linear Programming
Haruki Yokota, Hiroshi Higashi, Yuichi Tanaka, Gene Cheung
Graph Drawing Graph Structure Efficient Learning Graph Laplacian Iterative Optimization Balanced Approach Edge Weight Dependency Graph

September 10, 2024

Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer
Seyed Alireza Hosseini, Tam Thuc Do, Gene Cheung, Yuichi Tanaka
Neural Network Graph Laplacian Image Denoiser Graph Signal Denoising Denoising Performance Maximum a Posteriori

August 21, 2024

Chernoff Bounds for Tensor Expanders on Riemannian Manifolds Using Graph Laplacian Approximation
Shih-Yu Chang
Random Walk Riemannian Manifold Graph Laplacian Large Deviation Tail Bound Dimensional Random Vector

July 17, 2024

Dirac--Bianconi Graph Neural Networks -- Enabling Non-Diffusive Long-Range Graph Predictions
Christian Nauck, Rohan Gorantla, Michael Lindner, Konstantin Schürholt, Antonia S. J. S. Mey, Frank Hellmann
Graph Neural Network Message Passing Neural Network Graph Laplacian Long Term Prediction Graph Benchmark Graph Dynamic

May 2, 2024

Individual Fairness Through Reweighting and Tuning
Abdoul Jalil Djiberou Mahamadou, Lea Goetz, Russ Altman
Model Fairness Dynamic Reweighting Graph Laplacian Hyper Tune Inherent Bias Individual Fairness

April 25, 2024

Improved impedance inversion by deep learning and iterated graph Laplacian
Davide Bianchi, Florian Bossmann, Wenlong Wang, Mingming Liu
Deep Learning Graph Laplacian Tikhonov Regularization Impedance Inversion

April 23, 2024

All You Need is Resistance: On the Equivalence of Effective Resistance and Certain Optimal Transport Problems on Graphs
Sawyer Robertson, Zhengchao Wan, Alexander Cloninger
Graph Drawing Optimal Transport Wasserstein Distance Random Walk Graph Laplacian Effective Resistance Optimal Stopping

March 26, 2024

HERTA: A High-Efficiency and Rigorous Training Algorithm for Unfolded Graph Neural Networks
Yongyi Yang, Jiaming Yang, Wei Hu, Michał Dereziński
Graph Neural Network High Efficiency Graph Laplacian Training Algorithm Unfolded Graph Neural Network Spectral Sparsification

November 24, 2023

Disentangling the Spectral Properties of the Hodge Laplacian: Not All Small Eigenvalues Are Equal
Vincent P. Grande, Michael T. Schaub
Spectral Feature Graph Laplacian Smallest Eigenvalue Hodge Laplacian

October 16, 2023

Proper Laplacian Representation Learning
Diego Gomez, Michael Bowling, Marlos C. Machado
Robust Learning Graph Laplacian Large Scale Reinforcement Learning Laplacian Representation

September 2, 2023

Network Topology Inference with Sparsity and Laplacian Constraints
Jiaxi Ying, Xi Han, Rui Zhou, Xiwen Wang, Hing Cheung So
Sparsity Increase Sparse Graph Graph Laplacian Laplacian Related Constraint Network Topology Inference

August 7, 2023

Implicit Graph Neural Diffusion Networks: Convergence, Generalization, and Over-Smoothing
Guoji Fu, Mohammed Haroon Dupty, Yanfei Dong, Lee Wee Sun
Strong Generalization Early Stage Convergence Graph Neural Graph Laplacian Implicit Neural Network Undisciplined Over Smoothing Implicit Graph Neural Network

July 31, 2023

Semi-Supervised Laplacian Learning on Stiefel Manifolds
Chester Holtz, Pengwen Chen, Alexander Cloninger, Chung-Kuan Cheng, Gal Mishne
Semi Supervised Learning Semi Supervised Graph Laplacian Laplacian Matrix Laplacian Learning Stiefel Manifold

July 29, 2023

Multi-view Sparse Laplacian Eigenmaps for nonlinear Spectral Feature Selection
Gaurav Srivastava, Mahesh Jangid
Feature Selection Graph Laplacian Sparse Linear Regression Laplacian Matrix Laplacian Eigenmaps

July 5, 2023

Retinex-based Image Denoising / Contrast Enhancement using Gradient Graph Laplacian Regularizer
Yeganeh Gharedaghi, Gene Cheung, Xianming Liu
Graph Laplacian Surface Reflectance Contrast Enhancement Retinex Theory Graph Regularization Laplacian Regularization

June 27, 2023

Effective resistance in metric spaces
Robi Bhattacharjee, Alexander Cloninger, Yoav Freund, Andreas Oslandsbotn
Convergence Analysis Graph Laplacian Metric Space Edge Weight Effective Resistance

June 14, 2023

Multi-class Graph Clustering via Approximated Effective $p$-Resistance
Shota Saito, Mark Herbster
Average Approximation Graph Clustering Graph Laplacian Effective Resistance

Graph Laplacian

Papers

Improved convergence rate of kNN graph Laplacians

DLGNet: Hyperedge Classification through Directed Line Graphs for Chemical Reactions

Flexible Diffusion Scopes with Parameterized Laplacian for Heterophilic Graph Learning

Efficient Learning of Balanced Signed Graphs via Iterative Linear Programming

Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer

Chernoff Bounds for Tensor Expanders on Riemannian Manifolds Using Graph Laplacian Approximation

Dirac--Bianconi Graph Neural Networks -- Enabling Non-Diffusive Long-Range Graph Predictions

Individual Fairness Through Reweighting and Tuning

Improved impedance inversion by deep learning and iterated graph Laplacian

All You Need is Resistance: On the Equivalence of Effective Resistance and Certain Optimal Transport Problems on Graphs

HERTA: A High-Efficiency and Rigorous Training Algorithm for Unfolded Graph Neural Networks

Disentangling the Spectral Properties of the Hodge Laplacian: Not All Small Eigenvalues Are Equal

Proper Laplacian Representation Learning

Network Topology Inference with Sparsity and Laplacian Constraints

Implicit Graph Neural Diffusion Networks: Convergence, Generalization, and Over-Smoothing

Semi-Supervised Laplacian Learning on Stiefel Manifolds

Multi-view Sparse Laplacian Eigenmaps for nonlinear Spectral Feature Selection

Retinex-based Image Denoising / Contrast Enhancement using Gradient Graph Laplacian Regularizer

Effective resistance in metric spaces

Multi-class Graph Clustering via Approximated Effective $p$-Resistance