Accelerating Random Kaczmarz Algorithm Based on Clustering Information
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.
Cite
Text
Li et al. "Accelerating Random Kaczmarz Algorithm Based on Clustering Information." AAAI Conference on Artificial Intelligence, 2016. doi:10.1609/AAAI.V30I1.10217Markdown
[Li et al. "Accelerating Random Kaczmarz Algorithm Based on Clustering Information." AAAI Conference on Artificial Intelligence, 2016.](https://mlanthology.org/aaai/2016/li2016aaai-accelerating/) doi:10.1609/AAAI.V30I1.10217BibTeX
@inproceedings{li2016aaai-accelerating,
title = {{Accelerating Random Kaczmarz Algorithm Based on Clustering Information}},
author = {Li, Yujun and Mo, Kaichun and Ye, Haishan},
booktitle = {AAAI Conference on Artificial Intelligence},
year = {2016},
pages = {1823-1829},
doi = {10.1609/AAAI.V30I1.10217},
url = {https://mlanthology.org/aaai/2016/li2016aaai-accelerating/}
}