Max-Plus Algebraic Statistical Leverage Scores

James Hook

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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Abstract

The statistical leverage scores of a matrix A ∈ Rn×d record the degree of alignment between col(A) and the coordinate axes in Rn. These scores are used in random sampling algorithms for solving certain numerical linear algebra problems. In this paper we present a max-plus algebraic analogue of statistical leverage scores. We show that max-plus statistical leverage scores can be used to calculate the exact asymptotic behavior of the conventional statistical leverage scores of a generic radial basis function network (RBFN) matrix. We also show how max-plus statistical leverage scores can provide a novel way to approximate the conventional statistical leverage scores of a fixed, nonparametrized matrix.
Original languageEnglish
Pages (from-to)1410 - 1433
Number of pages23
JournalSIAM Journal On Matrix Analysis and Applications (SIMAX)
Volume38
Issue number4
DOIs
Publication statusPublished - 16 Nov 2017

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