arXiv Machine Learning
Fast Graph Laplacian Estimation using Effective Resistance
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arXiv Machine Learning
Sep 24
Graph Learning with Spectral Connectivity Priors for Scarce Data
The paper introduces Spectral Connectivity-Regularized Graph Learning (SCoGL), a method for learning sparse graphs from limited data by incorporating Laplacian spectral priors that promote global connectivity. SCoGL extends the graphical lasso objective with a connectivity prior derived from Laplacian eigenvalues and uses projected gradient descent with Armijo backtracking for optimization. Experiments demonstrate that SCoGL improves graph recovery and enhances downstream tasks such as graph signal denoising when observations are scarce.
arXiv AI
Sep 24
Scalable Subgraph Sampling via Resistance Curvature
The paper introduces a scalable subgraph sampling method that uses resistance curvature to guide the selection of nodes and edges for graph neural network training. It builds on ERC‑LG, a curvature approximation technique that employs Johnson‑Lindenstrauss projections and regularized multi‑GPU batched conjugate gradient solvers, thereby avoiding costly Laplacian pseudoinverse calculations and large embedding storage. Experiments demonstrate that ERC‑LG‑based sampling matches pseudoinverse‑based curvature numerically, runs faster than conjugate‑gradient‑only approaches, and achieves the best mean accuracy on six of seven real‑world node‑classification datasets.
arXiv Machine Learning
Aug 14
Difference-of-Convex Regularization for Graph Learning by Differentiable Programming
arXiv:2608. 12757v1 Announce Type: cross Abstract: Laplacian-regularized minimization is fundamental in signal processing and machine learning, but is limited by the dense and ill-conditioned nature of the graph Laplacian pseudoinverse.
arXiv Machine Learning
Jun 2
Advancing Local Clustering on Graphs via Compressive Sensing: Semi-supervised and Unsupervised Methods
arXiv:2504. 19419v3 Announce Type: replace Abstract: Local clustering aims to identify specific substructures within a large graph without any additional structural information of the graph.
arXiv Machine Learning
Sep 17
Provable Guarantees for Spectral Structured Prediction
The paper presents provable guarantees for a spectral method that recovers binary node labels on signed graphs with edge‑flip noise. It provides graph‑structure‑agnostic bounds on approximate inference accuracy and maximum angle deviation, using matrix concentration and eigenvector perturbation techniques. The results connect to the Cheeger constant and are validated with synthetic experiments, marking the first theoretical analysis of this spectral approach.
arXiv Machine Learning
Sep 3
From topology learning to graph generation: A unifying perspective
The article reviews the problem of learning graph structures from data, noting that research has traditionally split into two paths: inferring the topology of a single graph from observations on it, and learning a generative distribution from multiple observed graphs to sample new ones. It proposes a unified framework that treats both as inverse problems of a common graph generation process, reviews key methods, and discusses their interrelations, strengths, and limitations. The review highlights opportunities for cross‑paradigm integration and outlines future research directions.