Efficient coordinate-wise leading eigenvector computation

Jialei Wang; Weiran Wang; Dan Garber; Nathan Srebro

Efficient coordinate-wise leading eigenvector computation

Jialei Wang, Weiran Wang, Dan Garber, Nathan Srebro

Data and Decision Sciences

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We develop and analyze efficient "coordinate-wise" methods for finding the leading eigenvector, where each step involves only a vector-vector product. We establish global convergence with overall runtime guarantees that are at least as good as Lanczos's method and dominate it for slowly decaying spectrum. Our methods are based on combining a shift-and-invert approach with coordinate-wise algorithms for linear regression.

Original language	American English
Journal	arXiv e-prints
State	Published - 1 Feb 2017

Keywords

coordinate descent
eigenvalue problem
power method
shift-and-invert

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https://arxiv.org/abs/1702.07834v1

Cite this

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title = "Efficient coordinate-wise leading eigenvector computation",

abstract = "We develop and analyze efficient {"}coordinate-wise{"} methods for finding the leading eigenvector, where each step involves only a vector-vector product. We establish global convergence with overall runtime guarantees that are at least as good as Lanczos's method and dominate it for slowly decaying spectrum. Our methods are based on combining a shift-and-invert approach with coordinate-wise algorithms for linear regression.",

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T1 - Efficient coordinate-wise leading eigenvector computation

AU - Wang, Jialei

AU - Wang, Weiran

AU - Garber, Dan

AU - Srebro, Nathan

PY - 2017/2/1

Y1 - 2017/2/1

N2 - We develop and analyze efficient "coordinate-wise" methods for finding the leading eigenvector, where each step involves only a vector-vector product. We establish global convergence with overall runtime guarantees that are at least as good as Lanczos's method and dominate it for slowly decaying spectrum. Our methods are based on combining a shift-and-invert approach with coordinate-wise algorithms for linear regression.

AB - We develop and analyze efficient "coordinate-wise" methods for finding the leading eigenvector, where each step involves only a vector-vector product. We establish global convergence with overall runtime guarantees that are at least as good as Lanczos's method and dominate it for slowly decaying spectrum. Our methods are based on combining a shift-and-invert approach with coordinate-wise algorithms for linear regression.

KW - coordinate descent

KW - eigenvalue problem

KW - power method

KW - shift-and-invert

M3 - Article

JO - arXiv e-prints

JF - arXiv e-prints

ER -

Efficient coordinate-wise leading eigenvector computation

Abstract

Keywords

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