Low-Dimensional Embeddings for Gaussian Kernels on Manifolds

arXiv:2609.15179 · cs.CG, cs.LG · Submitted 2026-09-14 · Read on arXiv

cs.CG, cs.LG

Submitted: 2026-09-14

Updated: 2026-09-14

Comments: 57 pages, 3 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Ambient Dimension — 35× in this paper · explained in 1 episode
• Embeddings — 21× in this paper · explained in 2 episodes
• Persistent Homology — 21× in this paper · explained in 3 episodes
• Clustering — 18× in this paper · explained in 2 episodes
• Gaussian Kernel Power Distance — 9× in this paper
• Intrinsic Dimension — 8× in this paper · explained in 2 episodes
• Distance Preservation — 7× in this paper · explained in 2 episodes
• Hilbert Space — 6× in this paper · explained in 2 episodes
• Accuracy — 5× in this paper · explained in 1 episode
• Spectral clustering — 4× in this paper · explained in 2 episodes
• Alignment — 3× in this paper · explained in 1 episode
• Approximation Bound — 3× in this paper · explained in 1 episode
• Fidelity — 2× in this paper · explained in 2 episodes
• Reproducing Kernel Hilbert Space (RKHS) — 2× in this paper · explained in 3 episodes
• Sample Complexity — 2× in this paper · explained in 15 episodes
• Using Random Fourier Features — 2× in this paper
• Adaptation — 1× in this paper · explained in 1 episode
• Algorithmic Improvements — 1× in this paper · explained in 1 episode
• Combinatorial Optimization — 1× in this paper · explained in 2 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Distribution Matching — 1× in this paper · explained in 2 episodes
• Domain Adaptation — 1× in this paper · explained in 5 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 2 episodes
• Point Clouds — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nystr\"om Method, and Use of Kernels in Machine Learning: Tutorial and Survey
• Optimal Coreset for Gaussian Kernel Density Estimation

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