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Graph-structured data arise in a variety of real-world context ranging from sensor and transportation to biological and social networks. As a ubiquitous tool to process graph-structured data, spectral graph filters have been used to solve…
Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively…
Graph filters play a key role in processing the graph spectra of signals supported on the vertices of a graph. However, despite their widespread use, graph filters have been analyzed only in the deterministic setting, ignoring the impact of…
We develop a method for the accurate reconstruction of non-bandlimited finite rate of innovation signals on the sphere. For signals consisting of a finite number of Dirac functions on the sphere, we develop an annihilating filter based…
Graph-based clustering methods like spectral clustering and SpectralNet are very efficient in detecting clusters of non-convex shapes. Unlike the popular $k$-means, graph-based clustering methods do not assume that each cluster has a single…
Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…
Graph Comparative Learning (GCL) is a self-supervised method that combines the advantages of Graph Convolutional Networks (GCNs) and comparative learning, making it promising for learning node representations. However, the GCN encoders used…
A critical task in graph signal processing is to estimate the true signal from noisy observations over a subset of nodes, also known as the reconstruction problem. In this paper, we propose a node-adaptive regularization for graph signal…
We present a framework for the optimal filtering of spherical signals contaminated by realizations of an additive, zero-mean, uncorrelated and anisotropic noise process on the sphere. Filtering is performed in the wavelet domain given by…
In many applications, a dataset can be considered as a set of observed signals that live on an unknown underlying graph structure. Some of these signals may be seen as white noise that has been filtered on the graph topology by a graph…
This work studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph trend filtering framework to denoising…
Collaborative filtering is a popular approach in recommender systems, whose objective is to provide personalized item suggestions to potential users based on their purchase or browsing history. However, personalized recommendations require…
In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain…
Graph Neural Networks (GNNs) exploit signals from node features and the input graph topology to improve node classification task performance. However, these models tend to perform poorly on heterophilic graphs, where connected nodes have…
We study the problem of sampling and reconstruction of bandlimited graph signals where the objective is to select a node subset of prescribed cardinality that ensures interpolation of the original signal with the lowest reconstruction…
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate…
While deep learning (DL) architectures like convolutional neural networks (CNNs) have enabled effective solutions in image denoising, in general their implementations overly rely on training data, lack interpretability, and require tuning…
Graph signals are signals with an irregular structure that can be described by a graph. Graph neural networks (GNNs) are information processing architectures tailored to these graph signals and made of stacked layers that compose graph…
This paper focuses on spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. In machine learning settings where the dataset consists of signals…
Signal-processing on graphs has developed into a very active field of research during the last decade. In particular, the number of applications using frames constructed from graphs, like wavelets on graphs, has substantially increased. To…