Related papers: Localized Fourier Analysis for Graph Signal Proces…
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…
With the wide application of spectral and algebraic theory in discrete signal processing techniques in the field of graph signal processing, an increasing number of signal processing methods have been proposed, such as the graph Fourier…
While a common assumption in graph signal analysis is the smoothness of the signals or the band-limitedness of their spectrum, in many instances the spectrum of real graph data may be concentrated at multiple regions of the spectrum,…
In this paper, we present a novel generalization of the graph Fourier transform (GFT). Our approach is based on separately considering the definitions of signal energy and signal variation, leading to several possible orthonormal GFTs. Our…
Spectral graph neural networks learn graph filters, but their behavior with increasing depth and polynomial order is not well understood. We analyze these models in the graph Fourier domain, where each layer becomes an element-wise…
Spectral graph sparsification has emerged as a powerful tool in the analysis of large-scale networks by reducing the overall number of edges, while maintaining a comparable graph Laplacian matrix. In this paper, we present an efficient…
We present a fully non neural learning framework based on Graph Laplacian Wavelet Transforms (GLWT). Unlike traditional architectures that rely on convolutional, recurrent, or attention based neural networks, our model operates purely in…
We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by…
Defining a sound shift operator for signals existing on a certain graph structure, similar to the well-defined shift operator in classical signal processing, is a crucial problem in graph signal processing, since almost all operations, such…
In this paper, we present a signal processing framework for directed graphs. Unlike undirected graphs, a graph shift operator such as the adjacency matrix associated with a directed graph usually does not admit an orthogonal eigenbasis.…
Graph convolutional networks (GCNs) and its variants are designed for unsigned graphs containing only positive links. Many existing GCNs have been derived from the spectral domain analysis of signals lying over (unsigned) graphs and in each…
Vertex-frequency analysis, particularly the windowed graph Fourier transform (WGFT), is a significant challenge in graph signal processing. Tight frame theories is known for its low computational complexity in signal reconstruction, while…
Graph-based representations play a key role in machine learning. The fundamental step in these representations is the association of a graph structure to a dataset. In this paper, we propose a method that aims at finding a block sparse…
Transform-domain least mean squares (LMS) adaptive filters encompass the class of algorithms where the input data are subjected to a data-independent unitary transform followed by a power normalization stage as preprocessing steps. Because…
This letter extends the concept of graph-frequency to graph signals that evolve with time. Our goal is to generalize and, in fact, unify the familiar concepts from time- and graph-frequency analysis. To this end, we study a joint temporal…
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…
The graph Laplacian is a fundamental object in the analysis of and optimization on graphs. This operator can be extended to a simplicial complex $K$ and therefore offers a way to perform ``signal processing" on $p$-(co)chains of $K$.…
In the analysis of real-world data, extracting meaningful features from signals is a crucial task. This is particularly challenging when signals contain non-stationary frequency components. The Iterative Filtering (IF) method has proven to…
Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse…
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,…