提出非线性多视图CCA的可识别性理论，证明能准确找到共享信号子空间。
Provable Subspace Identification of Nonlinear Multi-view CCA
- 将多视图CCA重构为基不变子空间识别问题，避免了非线性混叠的病态解。
- 在三视图以上条件下，可精确分离跨视图共享子空间，剔除视图私有噪声。
- 理论给出有限样本下子空间误差界，适用于带先验和谱分离条件的数据。
我们研究在多视图设置下非线性典型相关分析（CCA）的可识别性，其中每个视图由未知非线性映射作用于共享潜在变量的线性混合加上视图私有噪声生成。不同于追求精确解混（在一般非线性混合下为病态问题），我们重新将多视图CCA视为基不变子空间识别问题。在合适的潜在先验和谱分离条件下，证明成对总体CCA目标函数可恢复相关信号子空间，至多存在视图内正交模糊。当视图数 $N \geq 3$ 时，多视图聚合可严格隔离所有视图共享的联合相关子空间，消除视图私有变异。通过谱扰动理论，将经验交叉协方差的集中性转化为显式的子空间误差界，建立了有限样本统计一致性保证。合成数据与渲染图像数据集上的实验验证了理论结论，并说明所假设条件的必要性。
原文摘要 · Abstract (English)
We investigate the identifiability of nonlinear canonical correlation analysis (CCA) in a multi-view setup, in which each view is generated by applying an unknown nonlinear map to a linear mixture of shared latent variables plus view-private noise. Rather than pursuing exact unmixing, which is known to be ill-posed under general nonlinear mixing, we instead reframe multi-view CCA as a basis-invariant subspace identification problem. Under suitable latent priors and spectral separation conditions, we prove that the pairwise population CCA objective recovers correlated signal subspaces up to view-wise orthogonal ambiguity. For $N \geq 3$ views, their multi-view aggregation provably isolates the jointly correlated subspaces shared across all views while eliminating view-private variation. We further establish finite-sample statistical 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 support our theoretical findings and illustrate the necessity of the assumed conditions.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。