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Graph signal processing (GSP) is an effective tool in dealing with data residing in irregular domains. In GSP, the optimal graph filter is one of the essential techniques, owing to its ability to recover the original signal from the…
Forecasting time series on graphs is a fundamental problem in graph signal processing. When each entity of the network carries a vector of values for each time stamp instead of a scalar one, existing approaches resort to the use of product…
A spectral sparsifier of a graph $G$ is a sparser graph $H$ that approximately preserves the quadratic form of $G$, i.e. for all vectors $x$, $x^T L_G x \approx x^T L_H x$, where $L_G$ and $L_H$ denote the respective graph Laplacians.…
This study addresses the issue of balancing graph summarization and graph change detection. Graph summarization compresses large-scale graphs into a smaller scale. However, the question remains: To what extent should the original graph be…
We propose a new framework for manifold denoising based on processing in the graph Fourier frequency domain, derived from the spectral decomposition of the discrete graph Laplacian. Our approach uses the Spectral Graph Wavelet transform in…
3D Point clouds (PCs) are commonly used to represent 3D scenes. They can have millions of points, making subsequent downstream tasks such as compression and streaming computationally expensive. PC sampling (selecting a subset of points) can…
Spectral Graph Neural Networks (GNNs), alternatively known as graph filters, have gained increasing prevalence for heterophily graphs. Optimal graph filters rely on Laplacian eigendecomposition for Fourier transform. In an attempt to avert…
We consider the problem of recovering random graph signals from nonlinear measurements. For this case, closed-form Bayesian estimators are usually intractable and even numerical evaluation of these estimators may be hard to compute for…
We study the problem of sampling and reconstructing spectrally sparse graph signals where the objective is to select a subset of nodes of prespecified cardinality that ensures interpolation of the original signal with the lowest possible…
Sensor placement plays a crucial role in graph signal recovery in underdetermined systems. In this paper, we present the graph-filtered regularized maximum likelihood (GFR-ML) estimator of graph signals, which integrates general graph…
A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated…
This paper focuses on spectral filters on graphs, namely filters defined as elementwise multiplication in the frequency domain of a graph. In many graph signal processing settings, it is important to transfer a filter from one graph to…
The graph Fourier transform (GFT) is a fundamental tool in graph signal processing and has recently been extended to the graph fractional Fourier transform (GFRFT). Existing sampling methods in the GFRFT domain are primarily designed to…
Graph Fourier transform (GFT) is a fundamental concept in graph signal processing. In this paper, based on singular value decomposition of Laplacian, we introduce a novel definition of GFT on directed graphs, and use singular values of…
We develop a framework for graph sparsification and sketching, based on a new tool, short cycle decomposition -- a decomposition of an unweighted graph into an edge-disjoint collection of short cycles, plus few extra edges. A simple…
Many tools from the field of graph signal processing exploit knowledge of the underlying graph's structure (e.g., as encoded in the Laplacian matrix) to process signals on the graph. Therefore, in the case when no graph is available, graph…
The notion of graph filters can be used to define generative models for graph data. In fact, the data obtained from many examples of network dynamics may be viewed as the output of a graph filter. With this interpretation, classical signal…
Superior performance and ease of implementation have fostered the adoption of Convolutional Neural Networks (CNNs) for a wide array of inference and reconstruction tasks. CNNs implement three basic blocks: convolution, pooling and pointwise…
The sampling of graph signals has recently drawn much attention due to the wide applications of graph signal processing. While a lot of efficient methods and interesting results have been reported to the sampling of band-limited or smooth…
Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon…