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Normalized Robust PCA With Adaptive Reconstruction Error Minimization
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DOI：10.1109/TKDE.2023.3325462.png)
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Abstract
En 中文
Principal component analysis (PCA) is one of the most versatile techniques for unsupervised dimension reduction, which is implemented as a fundamental preprocessing method in multiple tasks of statistics and machine learning research because of its efficiency. Nevertheless, researchers have concentrated on the identification of outliers that do not conform to the low-dimensional approximation through statistical methods, e.g., outlier rejection, without giving insights on each data point with a dynamic ratio of signal-to-noise components in the high-dimensional regimes. To characterize the dynamic nature of the principal component information, we propose a Normalized Robust PCA with Adaptive Reconstruction Error minimization model, which considers both the adaptive normalization technique and flexible weights learning simultaneously. With this configuration, the principal component information constantly adjusts the degree of sparsity for activated samples. In other words, the signal component's discrimination and noise information restriction could work cooperatively. Empirical studies on one synthetic dataset and several benchmarks demonstrate the effectiveness of our proposed method over existing outlier rejection methods.
Keywords:
Principal component analysis
Optimization
Image reconstruction
Covariance matrices
Maximum likelihood estimation
Maximum likelihood detection
Matrix decomposition
sigma - norm
adaptive weight
normalization
robust PCA
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