• Optics and Precision Engineering
  • Vol. 33, Issue 6, 961 (2025)
Qinting WU1, Xinjing Wang1, Jinyan PAN2, Haifeng ZHANG3..., Guifang SHAO1 and Yunlong GAO1,4,*|Show fewer author(s)
Author Affiliations
  • 1College of Mechanical Engineering, South China Univ. of Tech., Guangzhou5064, China
  • 2College of Information Engineering, Jimei University, FujianXiamen, 36101
  • 3School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, 201620
  • 4National Institute for Data Science in Health and Medicine, Xiamen University, FujianXiamen, 361102
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    DOI: 10.37188/OPE.20253306.0961 Cite this Article
    Qinting WU, Xinjing Wang, Jinyan PAN, Haifeng ZHANG, Guifang SHAO, Yunlong GAO. Robust principal component analysis based on soft mean filtering[J]. Optics and Precision Engineering, 2025, 33(6): 961 Copy Citation Text show less

    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 methods 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 information. This compromised the accurate identification and removal of noise and outliers, impacting subsequent algorithm performance. In response, we proposed a novel algorithm named Robust Principal Component 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, applying 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 frequencies 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.
    Qinting WU, Xinjing Wang, Jinyan PAN, Haifeng ZHANG, Guifang SHAO, Yunlong GAO. Robust principal component analysis based on soft mean filtering[J]. Optics and Precision Engineering, 2025, 33(6): 961
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