Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 220, Issue 1-2, Pages 456-463Publisher
ELSEVIER
DOI: 10.1016/j.cam.2007.08.023
Keywords
learning theory; reproducing kernel Hilbert spaces; derivative reproducing; representer theorem; Hermite learning and semi-supervised learning
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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.
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