Nearly Optimal Stochastic Approximation for Online Principal Subspace Estimation

Xin Liang National Chiao Tung University Zhen-Chen Guo National Chiao Tung University Ren-Cang Li University of Texas at Arlington Wen-Wei Lin National Chiao Tung University

Optimization and Control Data Analysis, Bio-Statistics, Bio-Mathematics mathscidoc:1711.27001

2018.8
Processing streaming data as they arrive is often necessary for high dimensional data analysis. In this paper, we analyze the convergence of a subspace online PCA iteration, as a followup of the recent work of Li, Wang, Liu, and Zhang [Math. Program., Ser. B, DOI 10.1007/s10107-017-1182-z] who considered the case for the most significant principal component only, i.e., a single vector. Under the sub-Gaussian assumption, we obtain a finite-sample error bound that closely matches the minimax information lower bound of Vu and Lei [Ann. Statist. 41:6 (2013), 2905-2947].
Principal component analysis, Principal component subspace, Stochastic approximation, High-dimensional data, Online algorithm, Finite-sample analysis
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  • Preprint, ver 2, 37 pages
@inproceedings{xin2018nearly,
  title={Nearly Optimal Stochastic Approximation for Online Principal Subspace Estimation},
  author={Xin Liang, Zhen-Chen Guo, Ren-Cang Li, and Wen-Wei Lin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20171118011441008772855},
  year={2018},
}
Xin Liang, Zhen-Chen Guo, Ren-Cang Li, and Wen-Wei Lin. Nearly Optimal Stochastic Approximation for Online Principal Subspace Estimation. 2018. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20171118011441008772855.
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