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

This paper addresses matrix approximation problems for matrices that arelarge, sparse and/or that are representations of large graphs. To tackle theseproblems, we consider algorithms that are based primarily on coarseningtechniques, possibly combined with random sampling. A multilevel coarseningtechnique is proposed which utilizes a hypergraph associated with the datamatrix and a graph coarsening strategy based on column matching. Theoreticalresults are established that characterize the quality of the dimensionreduction achieved by a coarsening step, when a proper column matching strategyis employed. We consider a number of standard applications of this technique aswell as a few new ones. Among the standard applications we first consider theproblem of computing the partial SVD for which a combination of sampling andcoarsening yields significantly improved SVD results relative to samplingalone. We also consider the Column subset selection problem, a popular low rankapproximation method used in data related applications, and show how multilevelcoarsening can be adapted for this problem. Similarly, we consider the problemof graph sparsification and show how coarsening techniques can be employed tosolve it. Numerical experiments illustrate the performances of the methods invarious applications.

Sampling and multilevel coarsening algorithms for fast matrix approximations