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Algorithmic Advances in Riemannian Geometry and Applications

  • Livre Relié
  • 208 Nombre de pages
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This book presents a selection of the most recent algorithmic advances in Riemannian geometry in the context of machine learning, ... Lire la suite
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Description

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.



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



Auteur

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.

Contenu

Introduction
Hà Quang Minh and Vittorio Murino

Bayesian Statistical Shape Analysis on the Manifold of Diffeomorphisms
Miaomiao Zhang and P. Thomas Fletcher

Sampling Constrained Probability Distributions using Spherical Augmentation
Shiwei Lan and Babak Shahbaba

Geometric Optimization in Machine Learning
Suvrit Sra and Reshad Hosseini

Positive Definite Matrices: Data Representation and Applications to Computer Vision
Anoop Cherian and Suvrit Sra

From Covariance Matrices to Covariance Operators: Data Representation from Finite to Infinite-Dimensional Settings
Hà Quang Minh and Vittorio Murino

Dictionary Learning on Grassmann Manifolds
Mehrtash Harandi, Richard Hartley, Mathieu Salzmann, and Jochen Trumpf

Regression on Lie Groups and its Application to Affine Motion Tracking
Fatih Porikli

An Elastic Riemannian Framework for Shape Analysis of Curves and Tree-Like Structures
Adam Duncan, Zhengwu Zhang, and Anuj Srivastava

Informations sur le produit

Titre: Algorithmic Advances in Riemannian Geometry and Applications
Éditeur:
Code EAN: 9783319450254
ISBN: 978-3-319-45025-4
Format: Livre Relié
Editeur: Springer, Berlin
Genre: Informatique
nombre de pages: 208
Poids: 516g
Taille: H16mm x B245mm x T172mm
Année: 2016
Auflage: 1st ed. 2016

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