Abstract: Integrative data analysis often requires separating shared from individual variations across multiple datasets, typically using the Joint and Individual Variation Explained (JIVE) model. Despite its popularity, theoretical insights into JIVE methods remain limited, particularly in the context of multiple matrices and varying degrees of subspace misalignment. In this talk, I will present new theoretical results on the Angle-based JIVE (AJIVE) method—a two-stage spectral algorithm. Specifically, we establish that AJIVE achieves decreasing estimation error with an increasing number of matrices in high signal-to-noise ratio (SNR) regimes. In contrast, AJIVE faces inherent limitations in low-SNR conditions, where estimation error remains persistently high. Complementary minimax lower bounds confirm AJIVE’s optimal performance at high SNR, while analysis of an oracle estimator highlights fundamental limitations of spectral methods at low SNR.