Convergence analysis of Oja’s iteration for solving online PCA with nonzero-mean samples  

作　　者：Siyun Zhou Yanqin Bai 

机构地区：[1]Department of Mathematics,Shanghai University,Shanghai 200444,China

出　　处：《Science China Mathematics》2021年第4期849-868,共20页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11771275)。

摘　　要：Principal component analysis(PCA)is one of the most popular multivariate data analysis techniques for dimension reduction and data mining,and is widely used in many fields ranging from industry and biology to finance and social development.When working on big data,it is of great necessity to consider the online version of PCA,in which only a small subset of samples could be stored.To handle the online PCA problem,Oja(1982)presented the stochastic power method under the assumption of zero-mean samples,and there have been lots of theoretical analysis and modified versions of this method in recent years.However,a common circumstance where the samples have nonzero mean is seldom studied.In this paper,we derive the convergence rate of a nonzero-mean version of Oja’s algorithm with diminishing stepsizes.In the analysis,we succeed in handling the dependency between each iteration,which is caused by the updated mean term for data centering.Furthermore,we verify the theoretical results by several numerical tests on both artificial and real datasets.Our work offers a way to deal with the top-1 online PCA when the mean of the given data is unknown.

关 键 词：online PCA Oja’s algorithm nonzero-mean samples convergence rate 

分 类 号：O212.4[理学—概率论与数理统计]