Algorithmic Advances in Riemannian Geometry and Applications

For Machine Learning, Computer Vision, Statistics, and Optimization
Softcover Nachdruck of the original 1. Auflage 2016
ISBN: 978-3-319-83190-9
Verlag: Springer International Publishing

Buch, Englisch, 208 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 3868 g

Reihe: Advances in Computer Vision and Pattern Recognition

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.

Zielgruppe

Research

Autoren/Hrsg.

Murino, Vittorio

Minh, Hà Quang

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Computer Vision
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
• Mathematik | Informatik Mathematik Stochastik
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Mustererkennung, Biometrik

Inhaltsverzeichnis

Introduction.- Bayesian Statistical Shape Analysis on the Manifold of Diffeomorphisms.- Sampling Constrained Probability Distributions using Spherical Augmentation.- Geometric Optimization in Machine Learning.- Positive Definite Matrices: Data Representation and Applications to Computer Vision.- From Covariance Matrices to Covariance Operators: Data Representation from Finite to Infinite-Dimensional Settings.- Dictionary Learning on Grassmann Manifolds.- Regression on Lie Groups and its Application to Affine Motion Tracking.- An Elastic Riemannian Framework for Shape Analysis of Curves and Tree-Like Structures.

Über Autor(innen)

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.