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New research explores convergence of graph Laplacians with symmetric divergence

By PulseAugur Editorial · [3 sources] ·

Researchers have published a paper detailing the convergence properties of graph Laplacians when constructed with a symmetric divergence on Riemannian submanifolds. The work establishes a bound relating the symmetric divergence to the geodesic distance, showing that under certain conditions, the difference between them is bounded by a power of the geodesic distance. This finding is crucial for the pointwise convergence of graph Laplacians built using these divergences, with specific examples discussed involving the Sinkhorn divergence on probability measures. AI

IMPACT This research contributes to the theoretical foundations of manifold learning algorithms, potentially impacting future developments in machine learning and data analysis.

RANK_REASON The cluster contains an academic paper published on arXiv.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 3 sources. How we write summaries →

New research explores convergence of graph Laplacians with symmetric divergence

COVERAGE [3]

  1. Hugging Face Daily Papers TIER_1 English(EN) ·

    On the convergence of graph Laplacians with a symmetric divergence

    When analyzing a manifold learning algorithm for data lying on a smooth, compact, connected Riemannian submanifold $(\mathcal{M}, g)$ of $\mathbb{R}^d$, a key estimate for the geodesic distance $d_g$ is that there exists $K > 0$ such that $0 \leq d_g(p, q)^2 - \|p-q\|^2 \leq K d_…

  2. arXiv stat.ML TIER_1 English(EN) · Liane Xu ·

    On the convergence of graph Laplacians with a symmetric divergence

    arXiv:2607.05892v1 Announce Type: new Abstract: When analyzing a manifold learning algorithm for data lying on a smooth, compact, connected Riemannian submanifold $(\mathcal{M}, g)$ of $\mathbb{R}^d$, a key estimate for the geodesic distance $d_g$ is that there exists $K > 0$ suc…

  3. arXiv stat.ML TIER_1 English(EN) · Liane Xu ·

    On the convergence of graph Laplacians with a symmetric divergence

    When analyzing a manifold learning algorithm for data lying on a smooth, compact, connected Riemannian submanifold $(\mathcal{M}, g)$ of $\mathbb{R}^d$, a key estimate for the geodesic distance $d_g$ is that there exists $K > 0$ such that $0 \leq d_g(p, q)^2 - \|p-q\|^2 \leq K d_…

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