Graph signal processing for visual analysis and data exploration

2019

The focus of Part I of this monograph has been on both the fundamental properties, graph topologies, and spectral representations of graphs. Part II embarks on these concepts to address the algorithmic and practical issues centered round data/signal processing on graphs, that is, the focus is on the analysis and estimation of both deterministic and random data on graphs. The fundamental ideas related to graph signals are introduced through a simple and intuitive, yet illustrative and general enough case study of multisensor temperature field estimation. The concept of systems on graph is defined using graph signal shift operators, which generalize the corresponding principles from traditional learning systems. At the core of the spectral domain representation of graph signals and systems is the Graph Discrete Fourier Transform (GDFT). The spectral domain representations are then used as the basis to introduce graph signal filtering concepts and address their design, including Chebys...

Journal Paper, 2022

It is a well-known fact that the world is developing rapidly, and a lot of development is made towards the betterment and to provide ease to human beings. Recently, a lot of research has been made on the latest signal processing to overcome the deficiencies that were part of classical signals processing. The new term of signal processing under discussion is called Graph Signal Processing (GSP). The essential purpose is to develop the equipment or the advanced devices that could analyze the data characterized on the irregular graphical domains. Here in this paper, the primary goal is to study and examine the essential concepts and the basic ingredients whose basis knowledge is compulsory while looking the Graph signal processing. After that, their linkups are discussed, or their association with the traditional digital signal processing along with the discussion of the basic concepts, which would focus on the ways that are recently being utilized to develop the graph signal processing toolbox. After that, the state-of-the-art topics are discussed, describing the challenges or barriers that occur while working on graph signal processing. Then, in the end, different applications are analyzed using the graph signal processing technique.

IEEE Signal Processing Magazine

Foundations and Trends® in Machine Learning, 2020

Graph signal processing(GSP) is a representation of data in graphical format with directed or undirected vertices. In many applications such as big data networks, economic and social networks analysis signals with graph is relevant. Harmonic analysis for processing the signals with spectral and algebric graphical thereotical concepts are merged and analyzed with respect to signal processing schemes on graphs. In this work, main challenges of GSP are discussed with Graph Spectral Domains (GSD) and when processing the signals on graph. The information is extracted efficiently from the highdimensional data by using operators of signals on graph and transformation of graph on signal are highlighted in this work. Finally, a brief discussion of open issues of GSP are reviewed.

arXiv (Cornell University), 2022

Graph signal processing (GSP) is a framework to analyze and process graph-structured data. Many research works focus on developing tools such as Graph Fourier transforms (GFT), filters, and neural network models to handle graph signals. Such approaches have successfully taken care of "signal processing" in many circumstances. In this paper, we want to put emphasis on "graph signals" themselves. Although there are characterizations of graph signals using the notion of bandwidth derived from GFT, we want to argue here that graph signals may contain hidden geometric information of the network, independent of (graph) Fourier theories. We shall provide a framework to understand such information, and demonstrate how new knowledge on "graph signals" can help with "signal processing".

2015

We present a framework for representing and modeling data on graphs. Based on this framework, we study three typical classes of graph signals: smooth graph signals, piecewise-constant graph signals, and piecewise-smooth graph signals. For each class, we provide an explicit definition of the graph signals and construct a corresponding graph dictionary with desirable properties. We then study how such graph dictionary works in two standard tasks: approximation and sampling followed with recovery, both from theoretical as well as algorithmic perspectives. Finally, for each class, we present a case study of a real-world problem by using the proposed methodology.

ArXiv, 2020

We present a short tutorial on to the use of the R gasper package. Gasper is a package dedicated to signal processing on graphs.

Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the spectrum of these matrices we show how to construct more general transforms, in particular wavelet-like transforms on graphs. For time-series, tomograms, a generalization of the Radon transforms to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signals and are robust in the presence of noise. Here the notion of tomogram transform is also extended to signals on arbitrary graphs