(a) (b)

The SVM model using the radial kernel function for the breast cancer data. (a)

istribution of the Gamma value variation. (b) The ROC curve for using the best

ue. The AUC was 0.996.

olynomial kernel is more suitable to the data in which variables

ete, especially binary. The difference between the radial basis

nd the polynomial kernel is the definition of the relationship

a data point and a support vector. Using the radial basis kernel,

onship between a data point and a support vector is defined by the

n distance, i.e., ‖ܠെܠ௡‖^૛. However, the relationship between a

t and a support vector is defined as a dot product when using the

ial kernel, i.e., ܠ^࢚ܠ௡. Figure 3.32(a) shows the ROC curve of a

odel using the polynomial kernel function constructed for the

ncer data, where both

and

ߙ

ߚ were optimised using a grid search

e degree parameter (d) was fixed at 3. Both

and

ߙ

ߚ were varied

1 to 0.1. The best ߙ value was 0.097 and the best ߚ value was

this breast cancer data using this SVM kernel function.

igmoid kernel function used in SVM is designed using two

rs shown below, where both ߙ and ߚ are two parameters,

ߖሺܠ, ܠ௡ሻൌ

1

1 ൅expሺെߙܠ^࢚ܠ௡െߚሻ

(3.71)

gmoid kernel has a similar property as the polynomial kernel. To

igmoid kernel function for a SVM model for the breast cancer

nd ߚ were also optimised via a grid search process. Both ߙ and ߚ