∈࣬^ௗ is the n^th basis function, x has the same dimension as ܠ௡,

࣬^ௗ, ߴ௡ and ݓ௡ are the n^th smoothing parameter and weighting

r, ࣡ሺ∙ሻ is the basis (normally Gaussian) function, and ݕො is the

tput or prediction for x. This transformation maps an original d-

nal data space (ܠ, ܠ௡∈࣬^ௗ) to a K-dimensional kernel space. It is

that this K-dimensional kernel space has a linearity property, i.e.,

elationship between a dependent variable or phenotype variable

he features or the basis function (࣡ሺ∙ሻ).

tablish a RBFNN model, the likelihood function is commonly

an objective function for classification problems. Suppose the

function is used by RBFNN for the output transformation based

ollowing definition, where the sigmoid output is treated as a

ty,

݌ሺܠ௡ሻൌ

1

1 ൅expሺെݕො௡ሻ

(3.39)

kelihood function for N data points is then defined as below using

oulli function [Uspensky, 1937]

ൌෑܲሺܠ௡|ݕ௡ሻ

ே

௡ୀଵ

ൌෑ݌ሺܠ௡ሻ^௬೙ሺ1 െ݌ሺܠ௡ሻሻ^ଵି௬೙

ே

௡ୀଵ

(3.40)

regression analysis problem, an error function shown below is

y used,

ߝൌ¹

ܰ^{෍ሺݕ௡െݕො௡ሻଶ}

ே

௡ୀଵ

(3.41)

NN has a wide application in many areas including

l/medical pattern analysis. For instance, RBFNN has been used

ne how pear rootstocks tissue culture media is formed [Jamshidi,

19] and to remove tomography ring artifacts [Chao and Kim,