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Full Description
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.
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.
This second edition has been revised and updated and has now been expanded to include new chapters on cutting-edge topics relevant to the analysis of graph signals such as machine learning.
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.
Contents
Part I: Introduction.- Introduction to graph signal processing.- Part II: Vertex-frequency theory.- Transformation from graphs to signals and back.- The spectral graph wavelet transform: Fundamental theory and fast computation.- Signal-adapted decomposition of graph signals.- Wavelets on graphs via deep learning.- Oversampled transforms for graph signals.- Spectral analysis on directed acyclic graphs.- Matched filtering on graphs.- A filtering framework for time-varying graph signals.- Vertex-frequency energy distributions.- Part III: Applications.- Flexible graph encoder-decoder for unsupervised anomaly detection.- Estimating the complexity of the cerebral cortex folding with a local shape spectral analysis.- Wavelet-based visual data exploration.- Graph-based wavelet multiresolution modeling of multivariate terrain data.
