caa a22 4500 467939497 CHVBK 20180406153008.0 cr unu---uuuuu 170328e20060701xx s 000 0 eng 10.1007/s10444-004-7616-1 doi (NATIONALLICENCE)springer-10.1007/s10444-004-7616-1 Linearly constrained reconstruction of functions by kernels with applications to machine learning [Elektronische Daten] [R. Schaback, J. Werner] This paper investigates the approximation of multivariate functions from data via linear combinations of translates of a positive definite kernel from a reproducing kernel Hilbert space. If standard interpolation conditions are relaxed by Chebyshev-type constraints, one can minimize the norm of the approximant in the Hilbert space under these constraints. By standard arguments of optimization theory, the solutions will take a simple form, based on the data related to the active constraints, called support vectors in the context of machine learning. The corresponding quadratic programming problems are investigated to some extent. Using monotonicity results concerning the Hilbert space norm, iterative techniques based on small quadratic subproblems on active sets are shown to be finite, even if they drop part of their previous information and even if they are used for infinite data, e.g., in the context of online learning. Numerical experiments confirm the theoretical results. Springer, 2006 positive definite radial basis functions nationallicence quadratic programming nationallicence kernel machines nationallicence machine learning nationallicence support vector machines nationallicence regression nationallicence Schaback R. Göttingen, Germany aut Werner J. Göttingen, Germany aut Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 237-258 1019-7168 25:1-3<237 2006 25 10444 https://doi.org/10.1007/s10444-004-7616-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7616-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Schaback R. Göttingen, Germany aut NATIONALLICENCE 700 1- Werner J. Göttingen, Germany aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 237-258 1019-7168 25:1-3<237 2006 25 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer