光学精密工程2025，Vol.33Issue(6)：961-978,18.DOI:10.37188/OPE.20253306.0961
基于Soft均值滤波的鲁棒主成分分析算法
Robust principal component analysis based on soft mean filtering
摘要
Abstract
Dimensionality reduction plays a pivotal role in data visualization and preprocessing.Principal Component Analysis(PCA),a common unsupervised dim-reduction method,encounters challenges in practical applications as it is highly sensitive to noise and outliers.To address this issue,robust PCA meth-ods had been developed,aiming to minimize the reconstruction errors induced by outliers.However,these methods frequently overlooked the local structure of data,resulting in a loss of critical structural in-formation.This compromised the accurate identification and removal of noise and outliers,impacting sub-sequent algorithm performance.In response,we proposed a novel algorithm named Robust Principal Com-ponent Analysis Based on Soft Mean Filtering(RPCA-SMF).RPCA-SMF employed soft mean filtering and incorporated noise treatment in two stages:before and after model learning.Specifically,it used mean filtering to identify noise by comparing a sample's deviation from its local mean to that of its neighbors,ap-plying soft weighting to samples.Subsequently,it leveraged the"discriminant knowledge"of noise from the first stage to process noise information.The mean filter preserved the overall silhouette information of the data.For samples identified as noise,RPCA-SMF emphasized the silhouette information at low fre-quencies rather than the high-frequency noise information.Thus,RPCA-SMF could effectively retain the useful data information.It also improved the ability to maintain the overall structural characteristics of the data.This made the algorithm robust and more generalizable.关键词
降维/无监督特征提取/主成分分析/Soft均值滤波/鲁棒性Key words
dimensionality reduction/unsupervised feature extraction/principal component analysis/soft mean filtering/robust分类
信息技术与安全科学引用本文复制引用
吴沁停,王新景,潘金艳,张海峰,邵桂芳,高云龙..基于Soft均值滤波的鲁棒主成分分析算法[J].光学精密工程,2025,33(6):961-978,18.基金项目
国家自然科学基金(No.42076058) （No.42076058）
福建省促进海洋与渔业产业高质量发展专项(No.FJHYF-ZH-2023-05) （No.FJHYF-ZH-2023-05）
福建省自然科学基金(No.2020J01713、No.2022J01061) （No.2020J01713、No.2022J01061）
广东省基础与应用基础研究基金(No.2024A1515011682) （No.2024A1515011682）
