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  • Book
  • © 2016

Algorithmic Advances in Riemannian Geometry and Applications

For Machine Learning, Computer Vision, Statistics, and Optimization

  • 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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eBook USD 129.00
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  • ISBN: 978-3-319-45026-1
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  • Tax calculation will be finalised during checkout
Softcover Book USD 169.99
Price excludes VAT (USA)
Hardcover Book USD 169.99
Price excludes VAT (USA)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiv
  2. Bayesian Statistical Shape Analysis on the Manifold of Diffeomorphisms

    • Miaomiao Zhang, P. Thomas Fletcher
    Pages 1-23
  3. Geometric Optimization in Machine Learning

    • Suvrit Sra, Reshad Hosseini
    Pages 73-91
  4. Dictionary Learning on Grassmann Manifolds

    • Mehrtash Harandi, Richard Hartley, Mathieu Salzmann, Jochen Trumpf
    Pages 145-172
  5. An Elastic Riemannian Framework for Shape Analysis of Curves and Tree-Like Structures

    • Adam Duncan, Zhengwu Zhang, Anuj Srivastava
    Pages 187-205
  6. Back Matter

    Pages 207-208

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.


Keywords

  • Riemannian Geometry
  • Machine Learning
  • Optimization
  • Statistics
  • Computer Vision

Reviews

“The book under review consists of eight chapters, each introducing techniques for solving problems on manifolds and illustrating these with examples. … reading this book would add to my collection of tools for working with data on manifolds and expose me to new problems treatable by these tools. … In each case an effort has been made to provide enough of the underlying theory supporting the techniques, with explicit references where the interested reader can go for further details.” (Tim Zajic, IAPR Newsletter, Vol. 39 (3), July, 2017)

Editors and Affiliations

  • Istituto Italiano di Tecnologia, Pattern Analysis and Computer Vision, Genoa, Italy

    Hà Quang Minh

  • Istituto Italiano di Tecnologia, Pattern Analysis and Computer Vision , Genoa, Italy

    Vittorio Murino

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

Buying options

eBook USD 129.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-45026-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 169.99
Price excludes VAT (USA)
Hardcover Book USD 169.99
Price excludes VAT (USA)