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Kernel Space-Based Dual-Weighted Robust Principal Component Analysis
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DOI：10.1007/s00357-026-09552-7.png)
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Abstract
En 中文
As the most popular unsupervised dimensionality reduction method, the existence of outliers easily distorts the subspace projection matrix learned in principal component analysis (PCA). Though many studies have attempted to improve its robustness, it is still facing challenges in how to characterize the sample quality in a more fine-grained way and how to enhance the capability to model data with non-linear structures. In this work, a novel kernel space-based dual-weighted robust principal component analysis (KDRPCA) is proposed by mapping data into kernel space and evaluating samples by employing the sample reconstruction errors as their quality metric. To be specific, samples are partitioned into outliers and normal samples by a binary weight descriptor, and the normal samples are further refined as positive and hard ones by a probabilistic weight vector, leading to a dual-weight strategy. This is completed in the mapped RKHS (reproducing kernel Hilbert space) by jointly measuring the reconstruction error of each sample and the optimal mean of all the weighted samples. As a consequence, the coupled improvements of noise control and kernel mapping enable KDRPCA to have enhanced robustness and non-linear modeling ability. To evaluate the effectiveness of KDRPCA, extensive experiments are conducted on both synthetic and benchmark datasets across multiple aspects, including non-linear modeling capability, evaluation on the rationality of sample weights, analysis of reconstruction errors, clustering performance, and robustness under different noise levels. The experimental results demonstrate that KDRPCA exhibits competitive performance compared to popular PCA variants.
Keywords:
Kernel space
Non-linear structures
Dimensionality reduction
Binary weight descriptor
Probabilistic weight descriptor
Journal
J
IF:
1.9
Papers:
36
Citations:
2.2K
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