Related papers: Stratified Graph Spectra
Dynamic graph signal processing provides a principled framework for analyzing time-varying data defined on irregular graph domains. However, existing joint time-vertex transforms such as the joint time-vertex fractional Fourier transform…
Graph signal processing (GSP) facilitates the analysis of high-dimensional data on non-Euclidean domains by utilizing graph signals defined on graph vertices. In addition to static data, each vertex can provide continuous time-series…
Current methods of graph signal processing rely heavily on the specific structure of the underlying network: the shift operator and the graph Fourier transform are both derived directly from a specific graph. In many cases, the network is…
We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we…
Spectral sparsification is a technique that is used to reduce the number of non-zero entries in a positive semidefinite matrix with little changes to its spectrum. In particular, the main application of spectral sparsification is to…
Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…
Spectral graph signal processing is traditionally built on self-adjoint Laplacians, where orthogonal eigenbases yield an energy-preserving Fourier transform and a variational frequency ordering via a real Dirichlet form. Directed networks…
In recent years, improvements in various image acquisition techniques gave rise to the need for adaptive processing methods, aimed particularly for large datasets corrupted by noise and deformations. In this work, we consider datasets of…
This paper introduces a novel graph signal processing framework for building graph-based models from classes of filtered signals. In our framework, graph-based modeling is formulated as a graph system identification problem, where the goal…
The work in this thesis concerns the investigation of eigenvalues of the Laplacian matrix, normalized Laplacian matrix, signless Laplacian matrix and distance signless Laplacian matrix of graphs. In Chapter 1, we present a brief…
Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic,…
In social settings, individuals interact through webs of relationships. Each individual is a node in a complex network (or graph) of interdependencies and generates data, lots of data. We label the data by its source, or formally stated, we…
Graph Convolutional Networks (GCNs) have fueled a surge of research interest due to their encouraging performance on graph learning tasks, but they are also shown vulnerability to adversarial attacks. In this paper, an effective graph…
Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational…
Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although time-varying signals are abundant in nature, in many practical scenarios the information of interest resides…
Recent spectral graph sparsification research allows constructing nearly-linear-sized subgraphs that can well preserve the spectral (structural) properties of the original graph, such as the first few eigenvalues and eigenvectors of the…
The emerging field of graph signal processing (GSP) allows to transpose classical signal processing operations (e.g., filtering) to signals on graphs. The GSP framework is generally built upon the graph Laplacian, which plays a crucial role…
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…
We characterize when the spectral variation of the signed Laplacian matrices is integral after a new edge is added to a signed graph. As an application, for every fixed signed complete graph, we fully characterize the class of signed graphs…
In the past decade, several multi-resolution representation theories for graph signals have been proposed. Bipartite filter-banks stand out as the most natural extension of time domain filter-banks, in part because perfect reconstruction,…