Related papers: SGL: Spectral Graph Learning from Measurements

This work introduces a highly-scalable spectral graph densification framework (SGL) for learning resistor networks with linear measurements, such as node voltages and currents. We show that the proposed graph learning approach is equivalent…

This paper introduces Polynomial Graphical Lasso (PGL), a new approach to learning graph structures from nodal signals. Our key contribution lies in modeling the signals as Gaussian and stationary on the graph, enabling the development of a…

Learning meaningful graphs from data plays important roles in many data mining and machine learning tasks, such as data representation and analysis, dimension reduction, data clustering, and visualization, etc. In this work, for the first…

Graph Neural Networks (GNNs) play a pivotal role in graph-based tasks for their proficiency in representation learning. Among the various GNN methods, spectral GNNs employing polynomial filters have shown promising performance on tasks…

Graphs have become pervasive tools to represent information and datasets with irregular support. However, in many cases, the underlying graph is either unavailable or naively obtained, calling for more advanced methods to its estimation.…

Spectral graph sparsification aims to find ultra-sparse subgraphs whose Laplacian matrix can well approximate the original Laplacian eigenvalues and eigenvectors. In recent years, spectral sparsification techniques have been extensively…

Graphs are central to modeling complex systems in domains such as social networks, molecular chemistry, and neuroscience. While Graph Neural Networks, particularly Graph Convolutional Networks, have become standard tools for graph learning,…

Spectral graph sparsification is a classical tool for reducing graph complexity while preserving Laplacian quadratic forms. In graph neural networks (GNNs), sparsification is often used to accelerate computation while maintaining predictive…

To improve the robustness of graph neural networks (GNN), graph structure learning (GSL) has attracted great interest due to the pervasiveness of noise in graph data. Many approaches have been proposed for GSL to jointly learn a clean graph…

We present GERN, a novel scalable framework for training GNNs in node classification tasks, based on effective resistance, a standard tool in spectral graph theory. Our method progressively refines the GNN weights on a sequence of random…

Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…

In this paper, motivated by network inference and tomography applications, we study the problem of compressive sensing for sparse signal vectors over graphs. In particular, we are interested in recovering sparse vectors representing the…

We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible…

Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…

We study resistance sparsification of graphs, in which the goal is to find a sparse subgraph (with reweighted edges) that approximately preserves the effective resistances between every pair of nodes. We show that every dense regular…

In this work we propose a random graph model that can produce graphs at different levels of sparsity. We analyze how sparsity affects the graph spectra, and thus the performance of graph neural networks (GNNs) in node classification on…

We propose a supervised learning approach for predicting an underlying graph from a set of graph signals. Our approach is based on linear regression. In the linear regression model, we predict edge-weights of a graph as the output, given a…

The eigendeomposition of nearest-neighbor (NN) graph Laplacian matrices is the main computational bottleneck in spectral clustering. In this work, we introduce a highly-scalable, spectrum-preserving graph sparsification algorithm that…

Recent spectral graph sparsification research allows constructing nearly-linear-sized subgraphs that can well preserve the spectral (structural) properties of the original graph, such as the first few eigenvalues and eigenvectors of the…

Representing a graph as a vector is a challenging task; ideally, the representation should be easily computable and conducive to efficient comparisons among graphs, tailored to the particular data and analytical task at hand. Unfortunately,…