A dictionary learning framework for graphs via filters and optimal transport
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
arXiv:2203. 04711v2 Announce Type: replace Abstract: We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem.
The paper reviews the use of optimal transport for comparing undirected, unweighted graphs, focusing on three main distances: Wasserstein, Gromov-Wasserstein, and Bures-Wasserstein. It discusses closed-form solutions for the Wasserstein distance in one dimension, how transport plans identify influential nodes after perturbations, and derives spectral bounds for the Bures-Wasserstein distance to avoid full decompositions. The authors evaluate these distances on synthetic clustering data and a real-world time‑series network for anomaly detection.
arXiv:2608.27500v3 Announce Type: replace-cross Abstract: Network comparison using optimal transport is a growing area of research in network science. Unlike standard graph metrics, optimal transport...
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:2607. 21263v1 Announce Type: new Abstract: Graph signal processing tasks that leverage spectral information typically assume access to the complete graph topology, which is often unavailable in practice.
arXiv:2505. 21285v5 Announce Type: replace Abstract: This work proposes a framework LGKDE that learns kernel density estimation for graphs.