Search for optimal parameter values of the RBF kernel SVM

Description

In this experiment RBF kernel SVMs are trained on the Ionosphere data set while the value of the parameter gamma of the RBF kernel and also the value of the parameter C are changed. The average classification error rate from 10-fold cross-validation is determined for each SVM. As a result, the values yielding the best average classification error rate will be returned. The following parameter values will be considered for C and gamma: C = 2^n, where -5 <= n <= 6, gamma = 2^m, where -10 <= m <= 4. Thus, the total number of parameter value combinations considered is 180.

Input

Ionosphere [UCI MLR]

Output

Figure 8.22. The optimal parameter values for the RBF kernel SVM.

The optimal parameter values for the RBF kernel SVM.

Figure 8.23. The classification accuracy of the RBF kernel SVM trained on the entire data set using the optimal parameter values.

The classification accuracy of the RBF kernel SVM trained on the entire data set using the optimal parameter values.

Interpretation of the results

The first figure shows that the best average classification error rate is achieved when the value of the parameter C is 16 and the value of the parameter gamma is 0.015625. Note that these parameter values can not be considered as the global optimum of the average classification error rate, since they were obtained by performing a grid search that examines only a few points of the search space.

The second figure shows that the RBF kernel SVM trained on the entire data set using the optimal parameter values performs very well.

Video

Workflow

svm_exp8.rmp

Keywords

SVM
supervised learning
error rate
classification
cross-validation
parameter optimization

Operators

Apply Model
Log
Multiply
Normalize
Optimize Parameters (Grid)
Performance (Classification)
Read CSV
Set Parameters
Support Vector Machine (LibSVM)
X-Validation