Manifold learning theory and applications. (2011)

• Record Type: Book
• Further Information: Note: [edited by] Yunqian Ma, Yun Fu.
• Other Names: Ma, Yunqian; Fu, Yun (Yun Raymond)
• Contents: Spectral Embedding Methods for Manifold Learning; Introduction; Spaces and Manifolds; Data on Manifolds; Linear Manifold Learning; Nonlinear Manifold Learning; Summary; Acknowledgment; ; Robust Laplacian Eigenmaps Using Global Information; Introduction; Graph Laplacian; Global Information of Manifold; Laplacian Eigenmaps with Global Information; Experiments; Summary; Bibliographical and Historical Remarks; ; Density Preserving Maps; Introduction; The Existence of Density Preserving Maps; Density Estimation on Submanifolds; Preserving the Estimated Density: The Optimization; Summary; Bibliographical and Historical Remarks; ; Sample Complexity in Manifold Learning; Introduction; Sample Complexity of Classification on a Manifold; Learning Smooth Class Boundaries; Sample Complexity of Testing the Manifold Hypothesis; Connections and Related Work; Sample Complexity of Empirical Risk Minimization; Relating Bounded Curvature to Covering Number; Class of Manifolds with a Bounded Covering Number; Fat-Shattering Dimension and Random Projections; Minimax Lower Bounds on the Sample Complexity; Algorithmic Implications; Summary; ; Manifold Alignment; Introduction; Formalization and Analysis; Variants of Manifold Alignment; Application Examples; Summary; Bibliographical and Historical Remarks; Acknowledgments; ; Large-scale Manifold Learning; Introduction; Background; Comparison of Sampling Methods; Large-Scale Manifold Learning; Summary; Bibliography and Historical Remarks; ; Metric and Heat Kernel; Introduction Theoretic Background; Discrete Heat Kernel; Heat Kernel Simplification; Numerical Experiments; Applications; Summary; Bibliographical and Historical Remarks ; ; Discrete Ricci Flow for Surface and 3-Manifold; Introduction; Theoretic Background; Surface Ricci Flow; 3-Manifold Ricci Flow; Applications; Summary; Bibliographical and Historical Remarks; ; 2D and 3D Objects Morphing Using Manifold Techniques; Introduction; Interpolation on Euclidean spaces; Generalization of Interpolation Algorithms on a Manifold M; Interpolation on SO(m); Application: The Motion of a Rigid Object in Space; Interpolation on Shape Manifold; Examples of Fitting Curves on Shape Manifolds; Summary; ; Learning Image Manifolds from Local Features; Introduction; Joint Feature-Spatial Embedding; Solving the Out-Of-Sample Problem; From Feature Embedding to Image Embedding; Applications; Summary; Bibliographical and Historical remarks; ; Human Motion Analysis Applications of Manifold Learning; Introduction; Learning A Simple Motion Manifold; Factorized Generative Models; Generalized Style Factorization; Solving for Multiple Factors; Examples; Summary; Bibliographical and Historical remarks
• Publisher Details: Place of publication not identified : CRC Press
• Publication Date: 2011
• Extent: 1 online resource, illustrations
• Subjects: 516.07; Manifolds (Mathematics)
• Languages: English
• ISBNs: 9781466558878; 1466558873
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.