鲁棒自适应概率加权主成分分析  

Robust PCA Using Adaptive Probability Weighting

作　　者：高云龙 罗斯哲 潘金艳[2] 陈柏华 张逸松 GAO Yun-Long;LUO Si-Zhe;PAN Jin-Yan;CHEN Bai-Hua;ZHANG Yi-Song(School of Aeronautics and Astronautics,Xiamen University,Xiamen 361102;School of Information Engineering,Jimei University,Xiamen 361021)

机构地区：[1]厦门大学航空航天学院,厦门361102 [2]集美大学信息工程学院,厦门361021

出　　处：《自动化学报》2021年第4期825-838,共14页Acta Automatica Sinica

基　　金：国家自然科学基金(61203176);福建省自然科学基金(2013J05098,2016J01756)资助。

摘　　要：主成分分析(Principal component analysis,PCA)是处理高维数据的重要方法.近年来,基于各种范数的PCA模型得到广泛研究,用以提高PCA对噪声的鲁棒性.但是这些算法一方面没有考虑重建误差和投影数据描述方差之间的关系;另一方面也缺少确定样本点可靠性(不确定性)的度量机制.针对这些问题,本文提出一种新的鲁棒PCA模型.首先采用L_(2,p)模来度量重建误差和投影数据的描述方差.基于重建误差和描述方差之间的关系建立自适应概率误差极小化模型,据此计算主成分对于数据描述的不确定性,进而提出了鲁棒自适应概率加权PCA模型(RPCA-PW).此外,本文还设计了对应的求解优化方案.对人工数据集、UCI数据集和人脸数据库的实验结果表明,RPCA-PW在整体上优于其他PCA算法.Principal component analysis(PCA)is an important method for processing high-dimensional data.In recent years,PCA models based on various norms have been extensively studied to improve the robustness.However,on the one hand,these algorithms do not consider the relationship between reconstruction error and covariance;on the other hand,they lack the uncertainty of considering the principal component to the data description.Aiming at these problems,this paper proposes a new robust PCA algorithm.Firstly,the L_(2,p)-norm is used to measure the reconstruction error and the description variance of the projection data.Based on the reconstruction error and the description variance,the adaptive probability error minimization model is established to calculate the uncertainty of the principal component s description of the data.Based on the uncertainty,the adaptive probability weighting PCA is established.The corresponding optimization method is designed.The experimental results of artificial data sets,UCI data sets and face databases show that RPCA-PW is superior than other PCA algorithms.

关 键 词：主成分分析 加权主成分分析 维数约简 鲁棒性 

分 类 号：TP311.13[自动化与计算机技术—计算机软件与理论]