Robust principal component analysis for non-centered data

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Robust principal component analysis for non-centered data

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Robust principal component analysis (RPCA) is an advanced variant of traditional PCA that effectively handles datasets contaminated with outliers or corrupted entries. While standard PCA assumes data is centered (zero mean) and sensitive to extreme values, RPCA decomposes a matrix into a low-rank component (representing the clean data) and a sparse component (capturing anomalies).

For non-centered data, RPCA requires careful adaptation. The key challenge lies in separating the inherent data structure from both the offset (non-zero mean) and sparse corruptions. Common approaches include: Pre-centering with Robust Estimators: Using median or other robust location estimates instead of the mean to center data before applying RPCA, reducing bias from outliers. Joint Optimization: Extending the RPCA objective function to simultaneously estimate the offset during decomposition, often through alternating minimization.

Applications span domains like image processing (removing shadows/occlusions) and sensor data analysis where centering assumptions fail. Unlike classical PCA, RPCA’s resistance to non-centered perturbations makes it invaluable for real-world, noisy datasets.