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 show how sparse or isoperimetric cuts of a probabilitydensity function relate to Cheeger cuts of its principal eigenfunction, forappropriate definitions of `sparse cut' and `principal eigenfunction'.  We construct these appropriate definitions of sparse cut and principaleigenfunction in the probability density setting. Then, we prove Cheeger andBuser type inequalities similar to those for the normalized graph Laplacian ofAlon-Milman. We demonstrate that no such inequalities hold for most priordefinitions of sparse cut and principal eigenfunction. We apply this result togenerate novel algorithms for cutting probability densities and clusteringdata, including a principled variant of spectral clustering.

Weighted Cheeger and Buser Inequalities, with Applications to Clustering and Cutting Probability Densities