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.
Graph signal processing tasks that leverage spectral information typically assume access to the complete graph topology, which is often unavailable in practice. We propose a systematic framework for subgraph filter learning (SFL), where subgraph-supported operators approximate ambient graph filters under partial observations.
arXiv:2606. 06364v1 Announce Type: new Abstract: Subgraph detection seeks to identify whether and where instances of query patterns occur within a larger graph.
The paper introduces a dictionary learning framework for probability measure-valued data by embedding measures into Hilbert spaces using features derived from optimal transport geometry. It learns data‑adapted dictionaries through sparse autoencoder parameterizations, yielding fast, scalable representations of probability measures as sparse finite‑dimensional codes. The authors demonstrate the method on hyperspectral images, geometric point clouds, and document embeddings from large language models, and provide generalization bounds and covering number results for optimal transport and entropic transport map dictionaries.
arXiv:2609.15437v1 Announce Type: cross Abstract: End-to-end Supervised Graph Prediction (SGP) requires a permutation-invariant loss to compare predicted and target graphs with arbitrary node orderin...
arXiv:2607. 03587v1 Announce Type: new Abstract: We propose NetinfoGC, a framework for graph classification that extends the Network Usable Information (NUI) paradigm to graph-level learning.
arXiv:2607. 06546v1 Announce Type: cross Abstract: Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models.