The embedding dimension of Laplacian eigenfunction maps

DOI10.1016/j.acha.2014.03.002zbMath1304.58016arXiv1605.01643OpenAlexW3098542052WikidataQ125800073 ScholiaQ125800073MaRDI QIDQ741268

Jonathan Bates

Publication date: 11 September 2014

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.01643

zbMATH Keywords

manifold learningspectral embeddingnonlinear dimensionality reductioneigenmapshape registrationdiffusion mapeigenfunction embeddingglobal point signatureheat kernel embedding

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items

Embedding Riemannian manifolds by the heat kernel of the connection Laplacian ⋮ Manifold embeddings by heat kernels of connection Laplacian ⋮ Manifold learning with arbitrary norms ⋮ Embeddings of Riemannian Manifolds with Heat Kernels and Eigenfunctions ⋮ Embeddings of Riemannian manifolds with finite eigenvector fields of connection Laplacian ⋮ Explore Intrinsic Geometry of Sleep Dynamics and Predict Sleep Stage by Unsupervised Learning Techniques ⋮ Wave-shape oscillatory model for nonstationary periodic time series analysis ⋮ Data-driven efficient solvers for Langevin dynamics on manifold in high dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hierarchical shape segmentation and registration via topological features of Laplace-Beltrami eigenfunctions
• A spectral notion of Gromov-Wasserstein distance and related methods
• Relating diameter and mean curvature for submanifolds of Euclidean space
• Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
• Spectral geometry: direct and inverse problems. With an appendix by G. Besson
• On the parabolic kernel of the Schrödinger operator
• \(C^ \alpha\)-compactness for manifolds with Ricci curvature and injectivity radius bounded below
• The connections between the order of smoothness of a surface and its metric
• Embedding Riemannian manifolds by their heat kernel
• Spectral convergence of Riemannian manifolds
• Convergence of Riemannian manifolds and Laplace operators. I
• Spectral convergence of Riemannian manifolds. II
• Consistency of spectral clustering
• Convergence of Riemannian manifolds and Laplace operators. II
• Diffusion maps
• Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels
• EMBEDDING RIEMANNIAN MANIFOLDS VIA THEIR EIGENFUNCTIONS AND THEIR HEAT KERNEL
• NON-RIGID SPECTRAL CORRESPONDENCE OF TRIANGLE MESHES
• Local and global analysis of eigenfunctions
• Heat Kernel Bounds on Hyperbolic Space and Kleinian Groups
• The Heat Kernel on Hyperbolic Space
• Some isoperimetric inequalities and eigenvalue estimates
• A lower bound for the heat kernel
• Some regularity theorems in riemannian geometry
• CONVERGENCE OF HEAT KERNELS ON A COMPACT MANIFOLD
• Structural, Syntactic, and Statistical Pattern Recognition
• Finiteness Theorems for Riemannian Manifolds