We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nystr\"om approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the training set. When building low-rank kernel approximations in KCCA, previous work mostly samples the landmarks uniformly at random from the training set. We propose novel strategies for sampling the landmarks non-uniformly based on a version of statistical leverage scores recently developed for kernel ridge regression. We study the approximation accuracy of the proposed non-uniform sampling strategy, develop an incremental algorithm that explores the path of approximation ranks and facilitates efficient model selection, and derive the kernel stability of out-of-sample mapping for our method. Experimental results on both synthetic and real-world datasets demonstrate the promise of our method.

本文研究了利用Nyström逼近进行大规模核正交主成分分析（KCCA）中的列选择问题，其中利用训练集的“地标”点逼近两个半正定核矩阵。我们提出了一种基于最近为核岭回归开发的统计杠杆得分版本的非均匀采样地标策略，研究了所提出的非均匀采样策略的逼近精度，并开发了一种增量算法，易于探索逼近排名的路径并促进有效的模型选择，并推导了我们方法的样本外映射的核稳定性。在合成数据和实际数据集上的实验结果表明了我们方法的潜力。

关于近似核规范相关分析中的列选择