Provable Subspace Identification of Nonlinear Multi-view CCA
This work addresses the challenge of identifying shared latent structures in nonlinear multi-view data, which is incremental as it builds on existing CCA methods by providing theoretical guarantees.
The paper tackles the identifiability of nonlinear Canonical Correlation Analysis (CCA) in multi-view setups by reframing it as a subspace identification problem, proving that multi-view CCA recovers correlated signal subspaces up to orthogonal ambiguity and isolates jointly correlated subspaces for N ≥ 3 views, with experiments validating the theory.
We investigate the identifiability of nonlinear Canonical Correlation Analysis (CCA) in a multi-view setup, where each view is generated by an unknown nonlinear map applied to a linear mixture of shared latents and view-private noise. Rather than attempting exact unmixing, a problem proven to be ill-posed, we instead reframe multi-view CCA as a basis-invariant subspace identification problem. We prove that, under suitable latent priors and spectral separation conditions, multi-view CCA recovers the pairwise correlated signal subspaces up to view-wise orthogonal ambiguity. For $N \geq 3$ views, the objective provably isolates the jointly correlated subspaces shared across all views while eliminating view-private variations. We further establish finite-sample consistency guarantees by translating the concentration of empirical cross-covariances into explicit subspace error bounds via spectral perturbation theory. Experiments on synthetic and rendered image datasets validate our theoretical findings and confirm the necessity of the assumed conditions.