Introduction to Graph Signal Processing

A text that explains the fundamentals and applications of graph signal processing, covering node domain processing, graph signal frequency, sampling, and representations, and how to choose a graph. It is essential reading for graduate and senior undergraduate students, researchers, and industry professionals, with numerous exercises and Matlab examples.

Format: Hardback
Length: 300 pages
Publication date: 09 June 2022
Publisher: Cambridge University Press

Graph signal processing (GSP) is a field that deals with the analysis and processing of graph data, which is often represented as a collection of nodes and edges. GSP has numerous applications in various fields, such as computer science, engineering, and social sciences. In this article, we will provide a comprehensive overview of GSP, including its fundamentals, applications, and recent developments.

Graphs are a fundamental data structure used to represent relationships between objects or entities. They can be used to model a wide range of real-world phenomena, such as social networks, transportation networks, and biological systems. Graph signal processing (GSP) is a subfield of signal processing that focuses on analyzing and processing graph data. GSP is particularly useful in scenarios where the relationships between objects or entities are complex and dynamic.

One of the key challenges in GSP is the representation of graph data. Graphs can be represented in various ways, such as adjacency matrices, edge lists, and graph structures. Adjacency matrices are a common representation of graphs, where each row represents a node and each column represents an edge. Edge lists, on the other hand, represent graphs as a collection of edges. Graph structures, such as graphs, trees, and networks, are more complex and can represent hierarchical relationships between objects or entities.

Another challenge in GSP is the processing of graph data. Graphs can be large and complex, making it challenging to process them using traditional signal processing techniques. GSP uses a variety of techniques, such as graph convolutional networks (GCNs), graph neural networks (GNNs), and spectral graph theory, to process graph data. GCNs are a type of neural network that is specifically designed for processing graph data. They use a graph-based representation of the data and apply convolutional operations to extract features from the graph. GNNs, on the other hand, are a type of neural network that is designed to process graph data in a similar way to how humans process visual data. They use a graph-based representation of the data and apply neural network operations to extract features from the graph. Spectral graph theory is a branch of graph theory that focuses on the analysis of graph signals, such as graph frequencies and graph coherences.

GSP has numerous applications in various fields, such as computer science, engineering, and social sciences. In computer science, GSP is used to analyze and process social networks, transportation networks, and other complex systems. For example, GCNs are used to analyze social networks and identify influential nodes, while GNNs are used to analyze images and videos and identify objects and scenes. In engineering, GSP is used to analyze and optimize transportation networks, such as road networks and power grids. For example, GCNs are used to analyze traffic patterns and optimize traffic flow, while GNNs are used to analyze sensor data and detect abnormal conditions in power grids. In social sciences, GSP is used to analyze and understand social networks, such as friendship networks and voting behavior. For example, GCNs are used to analyze social networks and identify communities, while GNNs are used to analyze social media data and identify trends and patterns.

In recent years, GSP has experienced significant developments, such as the use of deep learning techniques and the integration of graph data with other types of data, such as text and images. Deep learning techniques, such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs), are particularly useful in GSP because they can learn complex patterns and relationships from graph data. Integration of graph data with other types of data is also important because it can provide new insights and perspectives on complex systems. For example, combining graph data with text data can be used to analyze social media posts and identify sentiment and topic trends.

In conclusion, graph signal processing (GSP) is a field that deals with the analysis and processing of graph data, which is often represented as a collection of nodes and edges. GSP has numerous applications in various fields, such as computer science, engineering, and social sciences. GSP uses a variety of techniques, such as graph convolutional networks, graph neural networks, and spectral graph theory, to process graph data. In recent years, GSP has experienced significant developments, such as the use of deep learning techniques and the integration of graph data with other types of data.

ISBN-13: 9781108428132