Efficient coordinate-wise leading eigenvector computation

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 slow...

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Bibliographic Details
Main Authors Wang, Jialei, Wang, Weiran, Garber, Dan, Srebro, Nathan
Format Journal Article
LanguageEnglish
Published 25.02.2017
Subjects
Computer Science - Learning
Computer Science - Numerical Analysis
Statistics - Machine Learning
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Summary: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.
DOI:10.48550/arxiv.1702.07834