Table of contents

  1. Front Matter
    Pages i-xiv
  2. Miaomiao Zhang, P. Thomas Fletcher
    Pages 1-23
  3. Suvrit Sra, Reshad Hosseini
    Pages 73-91
  4. Mehrtash Harandi, Richard Hartley, Mathieu Salzmann, Jochen Trumpf
    Pages 145-172
  5. Adam Duncan, Zhengwu Zhang, Anuj Srivastava
    Pages 187-205
  6. Back Matter
    Pages 207-208

About this book

Introduction

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

Editors and affiliations

  • Hà Quang Minh
    • 1
  • Vittorio Murino
    • 2
  1. 1.Istituto Italiano di TecnologiaPattern Analysis and Computer VisionGenoaItaly
  2. 2.Istituto Italiano di TecnologiaPattern Analysis and Computer Vision GenoaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-45026-1
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-45025-4
  • Online ISBN 978-3-319-45026-1
  • Series Print ISSN 2191-6586
  • Series Online ISSN 2191-6594
  • About this book