# First Efficient Convergence for Streaming k-PCA: a Global, Gap-Free, and Near-Optimal Rate

26 Jul 2016Zeyuan Allen-ZhuYuanzhi Li

We study streaming principal component analysis (PCA), that is to find, in $O(dk)$ space, the top $k$ eigenvectors of a $d\times d$ hidden matrix $\bf \Sigma$ with online vectors drawn from covariance matrix $\bf \Sigma$. We provide $\textit{global}$ convergence for Oja's algorithm which is popularly used in practice but lacks theoretical understanding for $k>1$... (read more)

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