%0 Journal Article
	%A Wei Zhang and  Su-Yan Tang and  Yi-Fan Zhu and  Wei-Ping Wang
	%D 2010
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 41, 2010
	%T Comparative Studies of Support Vector Regression between Reproducing Kernel and Gaussian Kernel
	%U https://publications.waset.org/pdf/8559
	%V 41
	%X Support vector regression (SVR) has been regarded
as a state-of-the-art method for approximation and regression. The
importance of kernel function, which is so-called admissible support
vector kernel (SV kernel) in SVR, has motivated many studies
on its composition. The Gaussian kernel (RBF) is regarded as a
“best" choice of SV kernel used by non-expert in SVR, whereas
there is no evidence, except for its superior performance on some
practical applications, to prove the statement. Its well-known that
reproducing kernel (R.K) is also a SV kernel which possesses many
important properties, e.g. positive definiteness, reproducing property
and composing complex R.K by simpler ones. However, there are a
limited number of R.Ks with explicit forms and consequently few
quantitative comparison studies in practice. In this paper, two R.Ks,
i.e. SV kernels, composed by the sum and product of a translation
invariant kernel in a Sobolev space are proposed. An exploratory
study on the performance of SVR based general R.K is presented
through a systematic comparison to that of RBF using multiple
criteria and synthetic problems. The results show that the R.K is
an equivalent or even better SV kernel than RBF for the problems
with more input variables (more than 5, especially more than 10) and
higher nonlinearity.
	%P 507 - 515