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insight - Principal Component Analysis (PCA)
Black-Box k-to-1-PCA Reductions: Theory and Applications
The author explores black-box deflation methods for k-PCA algorithms, providing sharper bounds on approximation parameters.
Heteroskedastic PCA with Missing Data: Inference and Uncertainty Quantification
Valid inference on principal subspace and covariance matrix under heteroskedastic noise with missing data.
Heteroskedastic PCA with Missing Data: Inference and Uncertainty Quantification
Constructing confidence regions for PCA in high dimensions with missing data and heteroskedastic noise.
Unified Neural Model for Linear and Nonlinear Principal Component Analysis
The paper proposes a unified neural model, called σ-PCA, that can learn both linear and nonlinear PCA as single-layer autoencoders. The model allows nonlinear PCA to learn the first rotation that reduces dimensionality and orders by variances, in addition to the second rotation that maximizes statistical independence, eliminating the subspace rotational indeterminacy.
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