04730nam 22007455 450 991025501470332120260810140820.010.1007/978-3-319-45026-1(CKB)3710000000891738(DE-He213)978-3-319-45026-1(MiAaPQ)EBC4711787(PPN)258853328(PPN)196319994(EXLCZ)99371000000089173820161005d2016 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierAlgorithmic Advances in Riemannian Geometry and Applications For Machine Learning, Computer Vision, Statistics, and Optimization /edited by Hà Quang Minh, Vittorio Murino1st ed. 2016.Cham :Springer International Publishing :Imprint: Springer,2016.1 online resource (XIV, 208 p. 55 illus., 51 illus. in color.)Advances in Computer Vision and Pattern Recognition,2191-65943-319-45025-5 3-319-45026-3 Includes bibliographical references at the end of each chapters and index.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.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.Advances in Computer Vision and Pattern Recognition,2191-6594Pattern recognition systemsComputational intelligenceMathematical statisticsData processingComputer scienceMathematicsArtificial intelligenceMathematical statisticsAutomated Pattern RecognitionComputational IntelligenceStatistics and ComputingMathematical Applications in Computer ScienceArtificial IntelligenceProbability and Statistics in Computer SciencePattern recognition systems.Computational intelligence.Mathematical statisticsData processing.Computer scienceMathematics.Artificial intelligence.Mathematical statistics.Automated Pattern Recognition.Computational Intelligence.Statistics and Computing.Mathematical Applications in Computer Science.Artificial Intelligence.Probability and Statistics in Computer Science.516.373Minh Hà Quangedthttp://id.loc.gov/vocabulary/relators/edtMurino Vittorioedthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK9910255014703321Algorithmic Advances in Riemannian Geometry and Applications2156534UNINA