Related papers: Accelerated filtering on graphs using Lanczos meth…
We propose the Lanczos network (LanczosNet), which uses the Lanczos algorithm to construct low rank approximations of the graph Laplacian for graph convolution. Relying on the tridiagonal decomposition of the Lanczos algorithm, we not only…
Graph signal processing analyzes signals supported on the nodes of a graph by defining the shift operator in terms of a matrix, such as the graph adjacency matrix or Laplacian matrix, related to the structure of the graph. With respect to…
Graph-based spectral denoising is a low-pass filtering using the eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial filtering avoids costly computation of the eigendecomposition by projections onto suitable…
We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph…
Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the…
Our goal in this paper is the robust design of filters acting on signals observed over graphs subject to small perturbations of their edges. The focus is on developing a method to identify spectral and polynomial graph filters that can…
Partitioning a graph into three pieces, with two of them large and connected, and the third a small ``separator'' set, is useful for improving the performance of a number of combinatorial algorithms. This is done using the second…
Diffusing a graph signal at multiple scales requires computing the action of the exponential of several multiples of the Laplacian matrix. We tighten a bound on the approximation error of truncated Chebyshev polynomial approximations of the…
Modern data introduces new challenges to classic signal processing approaches, leading to a growing interest in the field of graph signal processing. A powerful and well established model for real world signals in various domains is sparse…
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…
Over the last decade, signal processing on graphs has become a very active area of research. Specifically, the number of applications, for instance in statistical or deep learning, using frames built from graphs, such as wavelets on graphs,…
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…
Data are represented as graphs in a wide range of applications, such as Computer Vision (e.g., images) and Graphics (e.g., 3D meshes), network analysis (e.g., social networks), and bio-informatics (e.g., molecules). In this context, our…
Graph Neural Networks (GNNs) excel in handling graph-structured data but often underperform in link prediction tasks compared to classical methods, mainly due to the limitations of the commonly used message-passing principle. Notably, their…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make 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…
Spectral graph convolution, an important tool of data filtering on graphs, relies on two essential decisions: selecting spectral bases for signal transformation and parameterizing the kernel for frequency analysis. While recent techniques…
In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…
We introduce a new notion of graph sparsificaiton based on spectral similarity of graph Laplacians: spectral sparsification requires that the Laplacian quadratic form of the sparsifier approximate that of the original. This is equivalent to…
We introduce Adaptive Spectral Shaping, a data-driven framework for graph filtering that learns a reusable baseline spectral kernel and modulates it with a small set of Gaussian factors. The resulting multi-peak, multi-scale responses…