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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.23785 |
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| _version_ | 1866914356444266496 |
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| author | Han, Zhiwei Matthes, Stefan Shen, Hao |
| author_facet | Han, Zhiwei Matthes, Stefan Shen, Hao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23785 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Provable Subspace Identification of Nonlinear Multi-view CCA Han, Zhiwei Matthes, Stefan Shen, Hao Machine Learning 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. |
| title | Provable Subspace Identification of Nonlinear Multi-view CCA |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.23785 |