2016/02/05 by Weiran Wang, Wang, Weiran
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #Face and Expression Recognition #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.1602.02172
arxiv created 2016/02/05 · openalex publication_date 2016/02/05 · arxiv updated 2016/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nyström 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.