Algorithmic advances in Riemannian geometry and applications : for machine learning, computer vision, statistics, and optimization

• 其他作者：
  • Minh, Ha Quang, editor.
  • Murino, Vittorio, editor.
  • SpringerLink (Online service)
• 其他題名：
  • Advances in computer vision and pattern recognition.
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Advances in computer vision and pattern recognition,
• 主題： Geometry, Riemannian. , Riemannian manifolds. , Machine learning. , Computer vision. , Statistics. , Optimization , Computer Science. , Pattern Recognition. , Computational Intelligence. , Statistics and Computing/Statistics Programs. , Mathematical Applications in Computer Science. , Artificial Intelligence (incl. Robotics) , Probability and Statistics in Computer Science.
• ISBN： 9783319450261 (electronic bk.) 、 9783319450254 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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.
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• 摘要註: 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.
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