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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We propose a quantum algorithm for training nonlinear support vector machines(SVM) for feature space learning where classical input data is encoded in theamplitudes of quantum states. Based on the classical SVM-perf algorithm ofJoachims, our algorithm has a running time which scales linearly in the numberof training examples $m$ (up to polylogarithmic factors) and applies to thestandard soft-margin $\ell_1$-SVM model. In contrast, while classical SVM-perfhas demonstrated impressive performance on both linear and nonlinear SVMs, itsefficiency is guaranteed only in certain cases: it achieves linear $m$ scalingonly for linear SVMs, where classification is performed in the original inputdata space, or for the special cases of low-rank or shift-invariant kernels.Similarly, previously proposed quantum algorithms either have super-linearscaling in $m$, or else apply to different SVM models such as the hard-marginor least squares $\ell_2$-SVM which lack certain desirable properties of thesoft-margin $\ell_1$-SVM model. We classically simulate our algorithm and giveevidence that it can perform well in practice, and not only for asymptoticallylarge data sets.

A quantum extension of SVM-perf for training nonlinear SVMs in almost linear time