Algorithmic Advances in Riemannian Geometry and Applications
For Machine Learning, Computer Vision, Statistics, and Optimization
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Beschreibung
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.
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 Includes supplementary material: sn.pub/extras
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Hà Quang Minh
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Riemannian Geometry Machine Learning Optimization Statistics Computer Vision
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“The book under review consists of eight chapters, each introducing techniques for solving problems on manifolds and illustrating these with examples. … reading this book would add to my collection of tools for working with data on manifolds and expose me to new problems treatable by these tools. … In each case an effort has been made to provide enough of the underlying theory supporting the techniques, with explicit references where the interested reader can go for further details.” (Tim Zajic, IAPR Newsletter, Vol. 39 (3), July, 2017)
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