We are interested in approximating vector-valued functions on a compact
set $ØmegaR^d$. We consider reproducing kernel Hilbert
spaces of $R^m$-valued functions which each admit a unique
matrix-valued reproducing kernel $k$. These spaces seem promising,
when modelling correlations between the target function components.
The approximation of a function is a linear combination of matrix-valued
kernel evaluations multiplied with coefficient vectors. To guarantee
a fast evaluation of the approximant the expansion size, i.e. the
number of centers $n$ is desired to be small. We thus present three
different greedy algorithms by which a suitable set of centers is
chosen in an incremental fashion: First, the $P$-Greedy which requires
no function evaluations, second and third, the $f$-Greedy and $f/P$-Greedy
which require function evaluations but produce centers tailored to
the target function. The efficiency of the approaches is investigated
on some data from an artificial model.
%0 Report
%1 wittwar2018greedy
%A Wittwar, Dominik
%A Haasdonk, Bernard
%D 2018
%K imported vorlaeufig
%T Greedy Algorithms for Matrix-Valued Kernels
%U http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1773
%X We are interested in approximating vector-valued functions on a compact
set $ØmegaR^d$. We consider reproducing kernel Hilbert
spaces of $R^m$-valued functions which each admit a unique
matrix-valued reproducing kernel $k$. These spaces seem promising,
when modelling correlations between the target function components.
The approximation of a function is a linear combination of matrix-valued
kernel evaluations multiplied with coefficient vectors. To guarantee
a fast evaluation of the approximant the expansion size, i.e. the
number of centers $n$ is desired to be small. We thus present three
different greedy algorithms by which a suitable set of centers is
chosen in an incremental fashion: First, the $P$-Greedy which requires
no function evaluations, second and third, the $f$-Greedy and $f/P$-Greedy
which require function evaluations but produce centers tailored to
the target function. The efficiency of the approaches is investigated
on some data from an artificial model.
@techreport{wittwar2018greedy,
abstract = {We are interested in approximating vector-valued functions on a compact
set $\Omega\subset \mathbb R^d$. We consider reproducing kernel Hilbert
spaces of $\mathbb R^m$-valued functions which each admit a unique
matrix-valued reproducing kernel $k$. These spaces seem promising,
when modelling correlations between the target function components.
The approximation of a function is a linear combination of matrix-valued
kernel evaluations multiplied with coefficient vectors. To guarantee
a fast evaluation of the approximant the expansion size, i.e. the
number of centers $n$ is desired to be small. We thus present three
different greedy algorithms by which a suitable set of centers is
chosen in an incremental fashion: First, the $P$-Greedy which requires
no function evaluations, second and third, the $f$-Greedy and $f/P$-Greedy
which require function evaluations but produce centers tailored to
the target function. The efficiency of the approaches is investigated
on some data from an artificial model.},
added-at = {2018-07-20T10:54:15.000+0200},
author = {Wittwar, Dominik and Haasdonk, Bernard},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/285f46a45ba75097c6c3a944bb2948ee6/mhartmann},
file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/WH18_www_greedy_matrix_valued.pdf:PDF},
institution = {University of Stuttgart},
interhash = {20670ff46be37fb46ac40641fcfbdcaf},
intrahash = {85f46a45ba75097c6c3a944bb2948ee6},
keywords = {imported vorlaeufig},
owner = {santinge},
timestamp = {2018-07-20T08:54:15.000+0200},
title = {Greedy Algorithms for Matrix-Valued Kernels},
url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1773},
year = 2018
}
