The main contribution of this paper is the derivation of non-asymptotic convergence rates for Nyström kernel canonical correlation analysis (CCA) in a setting of statistical learning. Our theoretical results reveal that, under certain conditions, Nyström kernel CCA can achieve a convergence rate comparable to that of the standard kernel CCA, while offering significant computational savings. This finding has important implications for the practical application of kernel CCA, particularly in scenarios where computational efficiency is crucial. Numerical experiments are provided to demonstrate the effectiveness of Nyström kernel CCA.

中文翻译：

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使用 Nyström 近似的高效核典型相关分析

本文的主要贡献是推导了统计学习环境中 Nyström 核典型相关分析 (CCA) 的非渐近收敛率。我们的理论结果表明，在某些条件下，Nyström 内核 CCA 可以实现与标准内核 CCA 相当的收敛速度，同时显着节省计算量。这一发现对于内核 CCA 的实际应用具有重要意义，特别是在计算效率至关重要的场景中。数值实验证明了 Nyström 核 CCA 的有效性。