An intuitive and accessible text explaining the fundamentals and applications of graph signal processing. Requiring only an elementary understanding of linear algebra, it covers both basic and advanced topics, including node domain processing, graph signal frequency, sampling, and graph signal representations, as well as how to choose a graph. Understand the basic insights behind key concepts and learn how graphs can be associated to a range of specific applications across physical, biological and social networks, distributed sensor networks, image and video processing, and machine learning. With numerous exercises and Matlab examples to help put knowledge into practice, and a solutions manual available online for instructors, this unique text is essential reading for graduate and senior undergraduate students taking courses on graph signal processing, signal processing, information processing, and data analysis, as well as researchers and industry professionals.

An intuitive, accessible text explaining the fundamentals and applications of signal processing on graphs. It covers basic and advanced topics, includes numerous exercises and Matlab examples, and is accompanied online by a solutions manual for instructors, making it essential reading for graduate students, researchers, and industry professionals.

This book introduces new methods to analyze vertex-varying graph signals. In many real-world scenarios, the data sensing domain is not a regular grid, but a more complex network that consists of sensing points (vertices) and edges (relating the sensing points). Furthermore, sensing geometry or signal properties define the relation among sensed signal points. Even for the data sensed in the well-defined time or space domain, the introduction of new relationships among the sensing points may produce new insights in the analysis and result in more advanced data processing techniques. The data domain, in these cases and discussed in this book, is defined by a graph. Graphs exploit the fundamental relations among the data points. Processing of signals whose sensing domains are defined by graphs resulted in graph data processing as an emerging field in signal processing. Although signal processing techniques for the analysis of time-varying signals are well established, the corresponding graph signal processing equivalent approaches are still in their infancy. This book presents novel approaches to analyze vertex-varying graph signals. The vertex-frequency analysis methods use the Laplacian or adjacency matrix to establish connections between vertex and spectral (frequency) domain in order to analyze local signal behavior where edge connections are used for graph signal localization. The book applies combined concepts from time-frequency and wavelet analyses of classical signal processing to the analysis of graph signals. Covering analytical tools for vertex-varying applications, this book is of interest to researchers and practitioners in engineering, science, neuroscience, genome processing, just to name a few. It is also a valuable resource for postgraduate students and researchers looking to expand their knowledge of the vertex-frequency analysis theory and its applications. The book consists of 15 chapters contributed by 41 leading researches in the field.

Aimed at readers with a good grasp of the fundamentals of data analytics, this book sets out the fundamentals of graph theory and the emerging mathematical techniques for the analysis of a wide range of data acquired on graph environments. This book will be a useful friend and a helpful companion to all involved in data gathering and analysis.

Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.

Graph spectral image processing is the study of imaging data from a graph frequency perspective. Modern image sensors capture a wide range of visual data including high spatial resolution/high bit-depth 2D images and videos, hyperspectral images, light field images and 3D point clouds. The field of graph signal processing – extending traditional Fourier analysis tools such as transforms and wavelets to handle data on irregular graph kernels – provides new flexible computational tools to analyze and process these varied types of imaging data. Recent methods combine graph signal processing ideas with deep neural network architectures for enhanced performances, with robustness and smaller memory requirements. The book is divided into two parts. The first is centered on the fundamentals of graph signal processing theories, including graph filtering, graph learning and graph neural networks. The second part details several imaging applications using graph signal processing tools, including image and video compression, 3D image compression, image restoration, point cloud processing, image segmentation and image classification, as well as the use of graph neural networks for image processing.

This book differs from the classical DSP book model pioneered by O/S. Includes chapters on DFT, Z-Transform and Filter Design. The book starts out with what one reviewer calls "fun topics", and DSP applications".

Focused on the mathematical foundations of social media analysis, Graph-Based Social Media Analysis provides a comprehensive introduction to the use of graph analysis in the study of social and digital media. It addresses an important scientific and technological challenge, namely the confluence of graph analysis and network theory with linear alge

This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems. The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications. The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications. This book has been adopted as a textbook at the following universities: ? University of Stuttgart, Germany Royal Institute of Technology, Sweden Johannes Kepler University, Austria Georgia Tech, USA University of Washington, USA Ohio University, USA

A digital filter can be pictured as a "black box" that accepts a sequence of numbers and emits a new sequence of numbers. In digital audio signal processing applications, such number sequences usually represent sounds. For example, digital filters are used to implement graphic equalizers and other digital audio effects. This book is a gentle introduction to digital filters, including mathematical theory, illustrative examples, some audio applications, and useful software starting points. The theory treatment begins at the high-school level, and covers fundamental concepts in linear systems theory and digital filter analysis. Various "small" digital filters are analyzed as examples, particularly those commonly used in audio applications. Matlab programming examples are emphasized for illustrating the use and development of digital filters in practice.