English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we improve the spectral convergence rates for graph-basedapproximations of Laplace-Beltrami operators constructed from random data. Weutilize regularity of the continuum eigenfunctions and strong pointwiseconsistency results to prove that spectral convergence rates are the same asthe pointwise consistency rates for graph Laplacians. In particular, for anoptimal choice of the graph connectivity $\varepsilon$, our results show thatthe eigenvalues and eigenvectors of the graph Laplacian converge to those ofthe Laplace-Beltrami operator at a rate of $O(n^{-1/(m+4)})$, up to logfactors, where $m$ is the manifold dimension and $n$ is the number of verticesin the graph. Our approach is general and allows us to analyze a large varietyof graph constructions that include $\varepsilon$-graphs and $k$-NN graphs.

Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-NN graphs