Algorithmic Advances in Riemannian Geometry and Applications, 1st ed. 2016 For Machine Learning, Computer Vision, Statistics, and Optimization Advances in Computer Vision and Pattern Recognition Series
Coordonnateurs : Minh Hà Quang, Murino Vittorio
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.
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
Adam Duncan, Zhengwu Zhang, and Anuj Srivastava
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.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
Date de parution : 10-2016
Ouvrage de 208 p.
15.5x23.5 cm
Disponible chez l'éditeur (délai d'approvisionnement : 15 jours).
Prix indicatif 147,69 €
Ajouter au panierDate de parution : 06-2018
Ouvrage de 208 p.
15.5x23.5 cm
Disponible chez l'éditeur (délai d'approvisionnement : 15 jours).
Prix indicatif 147,69 €
Ajouter au panierThème d’Algorithmic Advances in Riemannian Geometry and Applications :
Mots-clés :
Riemannian Geometry; Machine Learning; Optimization; Statistics; Computer Vision