R1范数约束的流形正则化最优均值主成分分析算法

Manifold Regularized Principal Component Analysis with Optimal Mean Using R1-norm

基于R1范数的主成分分析(R1-PCA)是一种鲁棒的主成分分析算法.但是R1-PCA并没有考虑样本间的流形结构;另外,由于R1-PCA是基于L2范数来对样本进行中心化的,使得其样本均值对于R1-PCA而言不是最优的.对此,提出一种R1范数约束的流形正则化最优均值主成分分析(R1-MRPCAOM)算法.通过把流形正则化项加入到R1-PCA的目标函数中,使得R1-M RPCAOM能保持样本的流形结构;通过把均值作为待求解的变量,从而给出相对于R1-M RPCAOM的最优均值.利用半二次优化技术,设计一种求解R1-MRPCAOM的高效算法并证明了其收敛性.在数据库上的实验表明,R1-MRPCAOM比传统的PCA和R1-PCA有着更好的性能.

R1-norm based principal component analysis （ R1 -PCA ） is a robust PCA algorithm. R1 -PCA, however, does not consider the manifold structure of data. Besides, the mean of the training samples used in R1 -PCA is not optimal for R1 -PCA since it computes its mean based on L2-norm. To address the problems of R1-PCA, the manifold regularized principal component analysis with optimal mean using Rl-norm （ R1-MRPCAOM） is proposed in this paper. R1-MRPCAOM can keep the manifold structure of data since it＇s objective function contains a manifold regularization tenn. The optimal mean for R1-MRPCAOM is also computed by assuming that the mean of the training samples is a variable. A half quadratic based efficient algorithm for R1-MRPCAOM with convergence analysis is also proposed in this paper. Experiment results on some real data sets demonstrate that R1-MRPCAOM can achieve much better per- formances than the conventional PCA and R1-PCA.