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arXiv · 1511.05362

Accelerating Random Kaczmarz Algorithm Based on Clustering Information

Yujun Li·Kaichun Mo·Haishan Ye
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Abstract

Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate for the exact solution onto that space to get a new estimate. Many vairants of Kaczmarz algorithms are proposed on how to choose better hyperplanes. Using the property of randomly sampled data in high-dimensional space, we propose an accelerated algorithm based on clustering information to improve block Kaczmarz and Kaczmarz via Johnson-Lindenstrauss lemma. Additionally, we theoretically demonstrate convergence improvement on block Kaczmarz algorithm.

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Yujun Li, Kaichun Mo, Haishan Ye. 2015-11-17. Accelerating Random Kaczmarz Algorithm Based on Clustering Information. https://arxiv.org/abs/1511.05362

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