Hyperparameters in SVMs are parameters that are not learned from the data but are set prior to the training process. They control the behavior of the SVM model and can significantly impact its performance. Here are some important hyperparameters in SVM:
- Kernel: The kernel function determines the type of decision boundary used by the SVM. Common kernel functions include the linear, polynomial, radial basis function (RBF), and sigmoid function. The choice of kernel depends on the data and problem at hand.
- Regularization parameter (C): Regularization is a technique used to prevent overfitting or underfitting of the model. Regularization methods help to control the complexity of the model and improve its generalization on unseen data.
For a binary classification problem, the decision boundary is a hyperplane that separates data into two classes. The margin is the distance between this hyperplane and the nearest data point from either class. The “width” of the margin is the actual numerical value of the distance or gap between the decision boundary and the nearest data point.
A wider margin implies a larger separation between classes, providing more room for potential misclassifications without affecting the decision boundary. The regularization parameter, often denoted as C, controls the trade-off between achieving a low training error rate and maintaining a wide margin. A smaller C value allows for more misclassifications but results in a larger margin, while a larger C value tries to minimize misclassifications at the cost of a narrower margin.
- Gamma (for RBF kernels): The gamma parameter influences the shape of the decision boundary for SVMs with the RBF kernel. It determines the reach of each training sample and affects the smoothness of the decision boundary. Higher gamma values tend to result in more complex decision boundaries.
- Degree (for polynomial kernels): The degree parameter specifies the degree of the polynomial kernel function. It determines the nonlinearity of the decision boundary. Higher degree values allow for more complex decision boundaries but may increase the risk of overfitting.
These hyperparameters need to be carefully tuned to achieve the best performance of the SVM model. Grid search, random search, or other optimization techniques can be employed to explore different combinations of hyperparameter values and select the optimal set.
To implement an SVM with the default hyperparameters, we will use the svm.SVC class from the scikit-learn library. We will first create an instance of the SVC class and then fit the training data to the classifier.
An instance of the SVC class is created using svm.SVC(). By not specifying any hyperparameters, it uses the default values for the kernel, regularization parameter (C), and other relevant parameters:
from sklearn import svm
# Create an instance of the SVC class with default hyperparameters
clf = svm.SVC()
The fit() function is used to fit the training data to the classifier:
# Fit the training data to the classifier
clf.fit(x_train, y_train)