On the convergence of graph Laplacians with a symmetric divergence

arXiv:2607.05892 · stat.ML, cs.LG · Submitted 2026-07-07 · Read on arXiv

Liane Xu

stat.ML, cs.LG

Submitted: 2026-07-07

Comments: 51 pages, 10 figures

Code: https://github.com/lzx23/graph_laplacians_w_sdiv

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

Terminology

• Optimal Transport — 22× in this paper · explained in 5 episodes
• Degeneracy — 14× in this paper · explained in 4 episodes
• Python Optimal Transport — 5× in this paper
• Regularization — 5× in this paper · explained in 3 episodes
• Dimensionality Reduction — 4× in this paper · explained in 2 episodes
• Fisher Information — 4× in this paper · explained in 4 episodes
• Clustering — 3× in this paper · explained in 2 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• Embeddings — 3× in this paper · explained in 2 episodes
• Sample Complexity — 3× in this paper · explained in 20 episodes
• Editor — 2× in this paper · explained in 2 episodes
• Generative Model — 2× in this paper · explained in 2 episodes
• Generative Models — 2× in this paper · explained in 3 episodes
• Gradient Flow — 2× in this paper · explained in 2 episodes
• Higher-order derivatives — 2× in this paper · explained in 2 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Universality — 2× in this paper · explained in 2 episodes
• Conservation Laws — 1× in this paper · explained in 3 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Entropy Regularization — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 14 episodes
• Kullback–Leibler Divergence — 1× in this paper · explained in 2 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• Spectral Clustering — 1× in this paper · explained in 3 episodes
• Wasserstein Distance — 1× in this paper · explained in 6 episodes

Sources

• Weak limits of entropy regularized Optimal Transport; potentials, plans and divergences
• Gradient Flows of Potential Energies in the Geometry of Sinkhorn Divergences
• Laplace Learning in Wasserstein Space
• Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributions
• Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds
• A kernel-based analysis of Laplacian Eigenmaps
• Principal Curves In Metric Spaces And The Space Of Probability Measures

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