Derivative reproducing properties for kernel methods in learning theory

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:220

Article

Zhou, Ding-Xuan

关键词: learning theory;    reproducing kernel Hilbert spaces;    derivative reproducing;    representer theorem;    Hermite learning and semi-supervised learning;   

DOI  :  10.1016/j.cam.2007.08.023

来源: Elsevier

【 摘 要 】

The regularity of functions from reproducing kernel Hilbert spaces (RKHSs) is studied in the setting of learning theory. We provide a reproducing property for partial derivatives up to order s when the Mercer kernel is C-2s. For such a kernel on a general domain we show that the RKHS can be embedded into the function space C-s. These observations yield a representer theorem for regularized learning algorithms involving data for function values and gradients. Examples of Hermite learning and semi-supervised learning penalized by gradients on data are considered. (c) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free