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

Research output: Contribution to journal › Conference 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	English
Pages (from-to)	806-820
Number of pages	15
Journal	Proceedings of Machine Learning Research
Volume	83
State	Published - 2018
Event	29th International Conference on Algorithmic Learning Theory, ALT 2018 - Lanzarote, Spain Duration: 7 Apr 2018 → 9 Apr 2018

ASJC Scopus subject areas

Artificial Intelligence
Software
Control and Systems Engineering
Statistics and Probability

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{\textquoteright}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.",

author = "Jialei Wang and Weiran Wang and Dan Garber and Nathan Srebro",

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AU - Garber, Dan

AU - Srebro, Nathan

PY - 2018

Y1 - 2018

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.

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VL - 83

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JO - Proceedings of Machine Learning Research

JF - Proceedings of Machine Learning Research

T2 - 29th International Conference on Algorithmic Learning Theory, ALT 2018

Y2 - 7 April 2018 through 9 April 2018

ER -

Efficient coordinate-wise leading eigenvector computation

Abstract

ASJC Scopus subject areas

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