Provable Subspace Identification of Nonlinear Multi-view CCA

• URL: http://arxiv.org/abs/2602.23785v1
• Date: Fri, 27 Feb 2026 08:27:01 GMT
• Title: Provable Subspace Identification of Nonlinear Multi-view CCA
• Abstract summary: We investigate the identifiability of nonlinear Canonical Correlation Analysis (CCA) in a multi-view setup.<n>We prove that, under suitable latent priors and spectral separation conditions, multi-view CCA recovers the pairwise correlated signal subspaces up to view-wise ambiguity.
• Score: 7.550362088105815
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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