Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity

@InProceedings{pmlr-v48-shamira16,
  title = 	 {Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity},
  author = 	 {Shamir, Ohad},
  booktitle = 	 {Proceedings of The 33rd International Conference on Machine Learning},
  pages = 	 {248--256},
  year = 	 {2016},
  editor = 	 {Balcan, Maria Florina and Weinberger, Kilian Q.},
  volume = 	 {48},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {New York, New York, USA},
  month = 	 {20--22 Jun},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v48/shamira16.pdf},
  url = 	 {https://proceedings.mlr.press/v48/shamira16.html},
  abstract = 	 {We study the convergence properties of the VR-PCA algorithm introduced by (Shamir, 2015) for fast computation of leading singular vectors. We prove several new results, including a formal analysis of a block version of the algorithm, and convergence from random initialization. We also make a few observations of independent interest, such as how pre-initializing with just a single exact power iteration can significantly improve the analysis, and what are the convexity and non-convexity properties of the underlying optimization problem.}
}