LEADER 05210nam 22007695 450 001 9910255014703321 005 20220404190250.0 024 7 $a10.1007/978-3-319-45026-1 035 $a(CKB)3710000000891738 035 $a(DE-He213)978-3-319-45026-1 035 $a(MiAaPQ)EBC4711787 035 $z(PPN)258853328 035 $a(PPN)196319994 035 $a(EXLCZ)993710000000891738 100 $a20161005d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgorithmic advances in Riemannian geometry and applications $efor machine learning, computer vision, statistics, and optimization /$fedited by Hà Quang Minh, Vittorio Murino 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XIV, 208 p. 55 illus., 51 illus. in color.) 225 1 $aAdvances in Computer Vision and Pattern Recognition,$x2191-6586 311 $a3-319-45025-5 311 $a3-319-45026-3 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aIntroduction -- 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. 330 $aThis book presents a selection of the most recent algorithmic advances in Riemannian geometry in the context of machine learning, statistics, optimization, computer vision, and related fields. The unifying theme of the different chapters in the book is the exploitation of the geometry of data using the mathematical machinery of Riemannian geometry. As demonstrated by all the chapters in the book, when the data is intrinsically non-Euclidean, the utilization of this geometrical information can lead to better algorithms that can capture more accurately the structures inherent in the data, leading ultimately to better empirical performance. This book is not intended to be an encyclopedic compilation of the applications of Riemannian geometry. Instead, it focuses on several important research directions that are currently actively pursued by researchers in the field. These include statistical modeling and analysis on manifolds,optimization on manifolds, Riemannian manifolds and kernel methods, and dictionary learning and sparse coding on manifolds. Examples of applications include novel algorithms for Monte Carlo sampling and Gaussian Mixture Model fitting,  3D brain image analysis,image classification, action recognition, and motion tracking. 410 0$aAdvances in Computer Vision and Pattern Recognition,$x2191-6586 606 $aPattern recognition 606 $aComputational intelligence 606 $aStatistics  606 $aComputer science?Mathematics 606 $aComputer mathematics 606 $aArtificial intelligence 606 $aMathematical statistics 606 $aPattern Recognition$3https://scigraph.springernature.com/ontologies/product-market-codes/I2203X 606 $aComputational Intelligence$3https://scigraph.springernature.com/ontologies/product-market-codes/T11014 606 $aStatistics and Computing/Statistics Programs$3https://scigraph.springernature.com/ontologies/product-market-codes/S12008 606 $aMathematical Applications in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/M13110 606 $aArtificial Intelligence$3https://scigraph.springernature.com/ontologies/product-market-codes/I21000 606 $aProbability and Statistics in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/I17036 615 0$aPattern recognition. 615 0$aComputational intelligence. 615 0$aStatistics . 615 0$aComputer science?Mathematics. 615 0$aComputer mathematics. 615 0$aArtificial intelligence. 615 0$aMathematical statistics. 615 14$aPattern Recognition. 615 24$aComputational Intelligence. 615 24$aStatistics and Computing/Statistics Programs. 615 24$aMathematical Applications in Computer Science. 615 24$aArtificial Intelligence. 615 24$aProbability and Statistics in Computer Science. 676 $a516.373 702 $aMinh$b Hà Quang$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aMurino$b Vittorio$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910255014703321 996 $aAlgorithmic Advances in Riemannian Geometry and Applications$92156534 997 $aUNINA