Related papers: M-Channel Critically Sampled Spectral Graph Filter…

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…

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…

Spectral Graph Neural Networks (GNNs) have achieved state-of-the-art results by defining graph convolutions in the spectral domain. A common approach, popularized by ChebyNet, is to use polynomial filters based on continuous orthogonal…

Designing distributed optimal controllers subject to communication constraints is a difficult problem unless structural assumptions are imposed on the underlying dynamics and information exchange structure, e.g., sparsity, delay, or spatial…

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…

Our capacity to learn representations from data is related to our ability to design filters that can leverage their coupling with the underlying domain. Graph filters are one such tool for network data and have been used in a myriad of…

Design of filters for graph signal processing benefits from knowledge of the spectral decomposition of matrices that encode graphs, such as the adjacency matrix and the Laplacian matrix, used to define the shift operator. For shift matrices…

Approximation-based spectral graph neural networks, which construct graph filters with function approximation, have shown substantial performance in graph learning tasks. Despite their great success, existing works primarily employ…

Filters are fundamental in extracting information from data. For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including convolutional neural…

Graph neural networks (GNNs) have become a workhorse approach for learning from data defined over irregular domains, typically by implicitly assuming that the data structure is represented by a homophilic graph. However, recent works have…

Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph…

A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that…

In this article we study the energy level spectrum of fractals which have block-hierarchical structures. We develop a method to study the spectral properties in terms of linearization of spectral decimation procedure and verify it…

In digital signal processing, shift-invariant filters can be represented as a polynomial expansion of a shift operation,that is, the Z-transform representation. When extended to graph signal processing (GSP), this would mean that a…

Graph signal processing (GSP) uses a shift operator to define a Fourier basis for the set of graph signals. The shift operator is often chosen to capture the graph topology. However, in many applications, the graph topology may be unknown a…

Spectral graph neural networks are proposed to harness spectral information inherent in graph-structured data through the application of polynomial-defined graph filters, recently achieving notable success in graph-based web applications.…

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…

Classical spectral graph theory relies on the symmetry of the adjacency and Laplacian operators, which guarantees orthogonal eigenbases and energy-preserving Fourier transforms. However, real-world networks are intrinsically directed and…

Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…

Dense prediction tasks have enjoyed a growing complexity of encoder architectures, decoders, however, have remained largely the same. They rely on individual blocks decoding intermediate feature maps sequentially. We introduce banks, shared…