Overview
- Showcases Riemannian geometry as a foundational mathematical framework for solving many problems in machine learning, statistics, optimization, computer vision, and related fields
- Describes comprehensively the state-of-the-art theory and algorithms in the Riemannian framework along with their concrete practical applications
- Written by leading experts in statistics, machine learning, optimization, pattern recognition, and computer vision
- Includes supplementary material: sn.pub/extras
Part of the book series: Advances in Computer Vision and Pattern Recognition (ACVPR)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book presents a selection of the most recent algorithmic advances in Riemannian geometry in the context of machine learning, statistics, optimization, computer vision, and related fields. The unifying theme of the different chapters in the book is the exploitation of the geometry of data using the mathematical machinery of Riemannian geometry. As demonstrated by all the chapters in the book, when the data is intrinsically non-Euclidean, the utilization of this geometrical information can lead to better algorithms that can capture more accurately the structures inherent in the data, leading ultimately to better empirical performance. This book is not intended to be an encyclopedic compilation of the applications of Riemannian geometry. Instead, it focuses on several important research directions that are currently actively pursued by researchers in the field. These include statistical modeling and analysis on manifolds,optimization on manifolds, Riemannian manifolds and kernel methods, and dictionary learning and sparse coding on manifolds. Examples of applications include novel algorithms for Monte Carlo sampling and Gaussian Mixture Model fitting, 3D brain image analysis,image classification, action recognition, and motion tracking.
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Editors and Affiliations
About the editors
Dr. Hà Quang Minh is a researcher in the Pattern Analysis and Computer Vision (PAVIS) group, at the Italian Institute of Technology (IIT), in Genoa, Italy.
Dr. Vittorio Murino is a full professor at the University of Verona Department of Computer Science, and the Director of the PAVIS group at the IIT.Bibliographic Information
Book Title: Algorithmic Advances in Riemannian Geometry and Applications
Book Subtitle: For Machine Learning, Computer Vision, Statistics, and Optimization
Editors: Hà Quang Minh, Vittorio Murino
Series Title: Advances in Computer Vision and Pattern Recognition
DOI: https://doi.org/10.1007/978-3-319-45026-1
Publisher: Springer Cham
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-45025-4Published: 21 October 2016
Softcover ISBN: 978-3-319-83190-9Published: 28 June 2018
eBook ISBN: 978-3-319-45026-1Published: 05 October 2016
Series ISSN: 2191-6586
Series E-ISSN: 2191-6594
Edition Number: 1
Number of Pages: XIV, 208
Number of Illustrations: 4 b/w illustrations, 51 illustrations in colour
Topics: Pattern Recognition, Computational Intelligence, Statistics and Computing/Statistics Programs, Mathematical Applications in Computer Science, Artificial Intelligence, Probability and Statistics in Computer Science