Algorithmic Advances in Riemannian Geometry and Applications

Vittorio Murino

ISBN 10: 3319450255 / ISBN 13: 9783319450254

Published by Springer International Publishing, Springer Nature Switzerland Okt 2016, 2016

About this Item

Neuware -This book presents a selection of the most recent algorithmic advances in Riemanniangeometry in the context of machine learning, statistics, optimization, computervision, and related fields. The unifying theme of the different chapters in the bookis the exploitation of the geometry of data using the mathematical machinery ofRiemannian geometry. As demonstrated by all the chapters in the book, when the datais intrinsically non-Euclidean, the utilization of this geometrical information can leadto better algorithms that can capture more accurately the structures inherent in thedata, leading ultimately to better empirical performance. This book is not intended tobe an encyclopedic compilation of the applications of Riemannian geometry. Instead, itfocuses on several important research directions that are currently actively pursued byresearchers in the field. These include statistical modeling and analysis on manifolds,optimization on manifolds, Riemannian manifolds and kernel methods, and dictionarylearning and sparse coding on manifolds. Examples of applications include novel algorithmsfor Monte Carlo sampling and Gaussian Mixture Model fitting, 3D brain image analysis,image classification, action recognition, and motion tracking.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 224 pp. Englisch.

Seller Inventory # 9783319450254

Bibliographic Details

• Title: Algorithmic Advances in Riemannian Geometry and Applications
• Publisher: Springer International Publishing, Springer Nature Switzerland Okt 2016
• Publication Date: 2016
• Language: English
• ISBN 10: 3319450255
• ISBN 13: 9783319450254
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 17D millimeters 241 millimeters width by 160 millimeters height by 17 millimeters depth
• Weight: 547 grams

About this title

Synopsis

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.

About the Author

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.