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

We study fast algorithms for computing fundamental properties of a positivesemidefinite kernel matrix $K \in \mathbb{R}^{n \times n}$ corresponding to $n$points $x_1,\ldots,x_n \in \mathbb{R}^d$. In particular, we consider estimatingthe sum of kernel matrix entries, along with its top eigenvalue andeigenvector.  We show that the sum of matrix entries can be estimated to $1+\epsilon$relative error in time $sublinear$ in $n$ and linear in $d$ for many popularkernels, including the Gaussian, exponential, and rational quadratic kernels.For these kernels, we also show that the top eigenvalue (and an approximateeigenvector) can be approximated to $1+\epsilon$ relative error in time$subquadratic$ in $n$ and linear in $d$.  Our algorithms represent significant advances in the best known runtimes forthese problems. They leverage the positive definiteness of the kernel matrix,along with a recent line of work on efficient kernel density estimation.

Faster Kernel Matrix Algebra via Density Estimation