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.

Introduces graph signal processing provides novel algorithms that can be used to analyze vertex-varying graph signals Shows how these methods can be applied to increase our understanding of the human brain, social networks, and genomics Includes new chapters on novel topics such as machine learning

Autorentext

Prof. Ljubi a Stankovic was born in Montenegro in 1960. He received the B.S. degree in EE from the University of Montenegro (UoM) with the Best Student at the University award, winning twice the EE student competition in mathematics in Yugoslavia. He obtained the M.S. degree in communications from the University of Belgrade and the Ph.D. in theory of electromagnetic waves from the UoM.

As Fulbright Grantee, he spent 1984 1985 academic year at the Worcester Polytechnic Institute, USA. In 1997 1999, he was on leave at the Ruhr University Bochum, Germany, supported by the Alexander von Humboldt Foundation. At the beginning of 2001, he was at the Technische Universiteit Eindhoven, The Netherlands, as Visiting Professor. He was Visiting Academic at the Imperial College, London, in 2012-2013. He was Rector of the UoM 2003-2008 and Ambassador of Montenegro to the United Kingdom, Ireland, and Iceland from 2011 to 2015. Prof. Stankovic is a Life Fellow of IEEE and a recipient of numerous awards, including the Best Paper Award from the European Association for Signal Processing in 2017 for a paper published in the Signal Processing, the IEEE Signal Processing Magazine Best Column Award for 2020, and the Outstanding Paper Award at IEEE ICASSP 2021.

Prof. Ervin Sejdic received B.E.Sc. and Ph.D. degrees in electrical engineering from the University of Western Ontario, London, Ontario, Canada, in 2002 and 2008, respectively. From 2008 to 2010, he was Postdoctoral Fellow at the University of Toronto with a cross-appointment at Bloorview Kids Rehab, Canada s largest children s rehabilitation teaching hospital. From 2010 until 2011, he was Research Fellow at Harvard Medical School with a cross-appointment at Beth Israel Deaconess Medical Center. In 2011, Prof. Sejdic joined the Department of Electrical and Computer Engineering at the University of Pittsburgh (Pittsburgh, PA, USA). In 2021, he joined the University of Toronto as Faculty Member. He is also Research Chair in Artificial Intelligence for Health Outcomes at North York General Hospital in Toronto.

Prof. Sejdic is Senior Member of IEEE and Recipient of many awards. In February 2016, President Obama named Dr. Sejdic as a recipient of the Presidential Early Career Award for Scientists and Engineers. In 2017, Dr. Sejdic was awarded the National Science Foundation CAREER Award. In 2018, he was awarded the Chancellor s Distinguished Research Award at the University of Pittsburgh.

Inhalt

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.