Optics and Precision Engineering, Volume. 33, Issue 6, 961(2025)
Robust principal component analysis based on soft mean filtering
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.
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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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Received: Oct. 23, 2024
Accepted: --
Published Online: Jun. 16, 2025
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