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Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
We introduce a graph renormalization procedure based on the coarse-grained Laplacian, which generates reduced-complexity representations for characteristic scales identified through the spectral gap. This method retains both diffusion…
Key to successfully deal with complex contemporary datasets is the development of tractable models that account for the irregular structure of the information at hand. This paper provides a comprehensive and unifying view of several…
Complex real-world phenomena are often modeled as dynamical systems on networks. In many cases of interest, the spectrum of the underlying graph Laplacian sets the system stability and ultimately shapes the matter or information flow. This…
Traditional directed graph signal processing generally depends on fixed representation matrices, whose rigid structures limit the model's ability to adapt to complex graph topologies. To address this issue, this study employed the unified…
We study optimal synchronization of networks of coupled phase oscillators. We extend previous theory for optimizing the synchronization properties of undirected networks to the important case of directed networks. We derive a generalized…
We introduce QuaterGCN, a spectral Graph Convolutional Network (GCN) with quaternion-valued weights at whose core lies the Quaternionic Laplacian, a quaternion-valued Laplacian matrix by whose proposal we generalize two widely-used…
The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to…
Matching articulated shapes represented by voxel-sets reduces to maximal sub-graph isomorphism when each set is described by a weighted graph. Spectral graph theory can be used to map these graphs onto lower dimensional spaces and match…
Fault detection has a long tradition: the necessity to provide the most accurate diagnosis possible for a process plant criticality is somehow intrinsic in its functioning. Continuous monitoring is a possible way for early detection.…
Approximations of Laplace-Beltrami operators on manifolds through graph Lapla-cians have become popular tools in data analysis and machine learning. These discretized operators usually depend on bandwidth parameters whose tuning remains a…
We consider the problem of inferring the unobserved edges of a graph from data supported on its nodes. In line with existing approaches, we propose a convex program for recovering a graph Laplacian that is approximately diagonalizable by a…
In a graph convolutional network, we assume that the graph $G$ is generated wrt some observation noise. During learning, we make small random perturbations $\Delta{}G$ of the graph and try to improve generalization. Based on quantum…
Recent advancements in Graph Neural Networks have led to state-of-the-art performance on graph representation learning. However, the majority of existing works process directed graphs by symmetrization, which causes loss of directional…
We investigate a scalable $M$-channel critically sampled filter bank for graph signals, where each of the $M$ filters is supported on a different subband of the graph Laplacian spectrum. For analysis, the graph signal is filtered on each…
We study $\Gamma$-convergence of graph Dirichlet energies and spectral convergence of graph Laplacians on unions of intersecting manifolds of potentially different dimensions. Our investigation is motivated by problems of machine learning,…
Graph neural networks are recognized for their strong performance across various applications, with the backpropagation algorithm playing a central role in the development of most GNN models. However, despite its effectiveness, BP has…
In data science, hypergraphs are natural models for data exhibiting multi-way relations, whereas graphs only capture pairwise. Nonetheless, many proposed hypergraph neural networks effectively reduce hypergraphs to undirected graphs via…
Generic deep learning (DL) networks for image restoration like denoising and interpolation lack mathematical interpretability, require voluminous training data to tune a large parameter set, and are fragile in the face of covariate shift.…