期刊
MATHEMATICAL PROGRAMMING
卷 167, 期 1, 页码 75-97出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-017-1182-z
关键词
Principal component analysis; Stochastic approximation; Nonconvex optimization; Stochastic gradient method; High-dimensional data; Online algorithm; Finite-sample analysis
Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests. Despite its rich applications, theoretical convergence analysis remains largely open. In this paper, we cast online PCA into a stochastic nonconvex optimization problem, and we analyze the online PCA algorithm as a stochastic approximation iteration. The stochastic approximation iteration processes data points incrementally and maintains a running estimate of the principal component. We prove for the first time a nearly optimal finite-sample error bound for the online PCA algorithm. Under the subgaussian assumption, we show that the finite-sample error bound closely matches the minimax information lower bound.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据