Adaptive Invariant PCA from Augmentation Portfolios

Learning from an augmentation collection requires knowing which background variation it exposes and how strongly to suppress it. We study signal-preserving linear views with correlated backgrounds and shared noise. Complementary channels can identify the background space even when every pair is insufficient; we characterize their required number. We propose Adaptive Invariance PCA (AIPCA), a matrix-power path connecting pooled PCA, normalized alignment, and a limit that suppresses variation across views. Under complete coverage, its population limit eliminates background while retaining all signal coordinates when signal and background spaces are disjoint. Proportional-dimensional risk theory explains the tradeoff between background suppression and estimation error: intermediate powers can outperform the reference methods, whereas sufficiently strong signals favor pooled PCA. Source-wise validation selects the power using covariance profiles and paired comparisons with a reconstruction reference. Synthetic and controlled real-image experiments examine coverage, risk predictions, and adaptation to the available views.