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With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned…
We propose a framework for generalized sampling of graph signals that parallels sampling in shift-invariant (SI) subspaces. This framework allows for arbitrary input signals, which are not constrained to be bandlimited. Furthermore, the…
We study the clustering of bipartite graphs and Boolean matrix factorization in data streams. We consider a streaming setting in which the vertices from the left side of the graph arrive one by one together with all of their incident edges.…
Wireless networks are inherently graph-structured, which can be utilized in graph representation learning to solve complex wireless network optimization problems. In graph representation learning, feature vectors for each entity in the…
Verifying graph algorithms has long been considered challenging in separation logic, mainly due to structural sharing between graph subcomponents. We show that these challenges can be effectively addressed by representing graphs as a…
The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful…
The construction of a meaningful graph topology plays a crucial role in the effective representation, processing, analysis and visualization of structured data. When a natural choice of the graph is not readily available from the data sets,…
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…
This paper introduces a design method for densergraph-frequency graph Fourier frames (DGFFs) to enhance graph signal processing and analysis. The graph Fourier transform (GFT) enables us to analyze graph signals in the graph spectral domain…
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…
Do users from Carnegie Mellon University form social communities on Facebook? Do signal processing researchers from tightly collaborate with each other? Do Chinese restaurants in Manhattan cluster together? These seemingly different…
Motivated by the need to extract meaning from large amounts of complex structured data, we consider three critical problems on graphs: localization, decomposition, and dictionary learning of piecewise-constant signals. These graph-based…
Graph signal processing uses the graph eigenvector basis to analyze signals. However, these graph eigenvectors are typically linearly ordered (by total variation), which may not be reasonable for many graph structures. There have been…
Inthischapterwediscusshowtolearnanoptimalmanifoldpresentationto regularize nonegative matrix factorization (NMF) for data representation problems. NMF,whichtriestorepresentanonnegativedatamatrixasaproductoftwolowrank nonnegative matrices,…
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…
We study the localization of a cluster of activated vertices in a graph, from adaptively designed compressive measurements. We propose a hierarchical partitioning of the graph that groups the activated vertices into few partitions, so that…
This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…
We consider weighted tiling systems to represent functions from graphs to a commutative semiring such as the Natural semiring or the Tropical semiring. The system labels the nodes of a graph by its states, and checks if the neighbourhood of…
This document introduces the Graph Signal Processing Toolbox (GSPBox) a framework that can be used to tackle graph related problems with a signal processing approach. It explains the structure and the organization of this software. It also…
As irregularly structured data representations, graphs have received a large amount of attention in recent years and have been widely applied to various real-world scenarios such as social, traffic, and energy settings. Compared to…