Canonical kernel dimension reduction

• Published in: Computational statistics & data analysis Vol. 107; pp. 131 - 148
• Main Authors: Tao, Chenyang, Feng, Jianfeng
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2017
• Subjects: Canonical correlation analysis; Canonical functions; Kernel dimension reduction; Krylov subspace; Reproducing kernel Hilbert space; Sufficient dimension reduction; Sufficient dimension reduction; Canonical functions; Kernel dimension reduction; Reproducing kernel Hilbert space; Krylov subspace; Canonical correlation analysis
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2016.10.003

A new kernel dimension reduction (KDR) method based on the gradient space of canonical functions is proposed for sufficient dimension reduction (SDR). Similar to existing KDR methods, this new method achieves SDR for arbitrary distributions, but with more flexibility and improved computational efficiency. The choice of loss function in cross-validation is discussed, and a two-stage screening procedure is proposed. Empirical evidence shows that the new method yields favorable performance, both in terms of accuracy and scalability, especially for large and more challenging datasets compared with other distribution-free SDR methods. •A new sufficient dimension reduction method based on kernel canonical functions.•This new method is distribution free and highly scalable.•We give theoretical proof of the sufficient dimension reduction property.•We present efficient algorithms and discuss the choice of loss function.•Extensive experiments demonstrate its advantage over existing approaches.