Kernel Function is a method used to take data as input and transform it into the required form of processing data. “Kernel” is used due to a set of mathematical functions used in Support Vector Machine providing the window to manipulate the data. So, Kernel Function generally transforms the training set of data so that a non-linear decision surface is able to transform to a linear equation in a higher number of dimension spaces. Basically, It returns the inner product between two points in a standard feature dimension.
Standard Kernel Function Equation : 
Major Kernel Functions :-
For Implementing Kernel Functions, first of all, we have to install the “scikit-learn” library using the command prompt terminal:
pip install scikit-learn
- Gaussian Kernel: It is used to perform transformation when there is no prior knowledge about data.
- Gaussian Kernel Radial Basis Function (RBF): Same as above kernel function, adding radial basis method to improve the transformation.
Gaussian Kernel Graph
Code:
python3
from sklearn.svm import SVCclassifier = SVC(kernel ='rbf', random_state = 0) # training set in x, y axisclassifier.fit(x_train, y_train) |
- Sigmoid Kernel: this function is equivalent to a two-layer, perceptron model of the neural network, which is used as an activation function for artificial neurons.
Sigmoid Kernel Graph
Code:
python3
from sklearn.svm import SVCclassifier = SVC(kernel ='sigmoid')classifier.fit(x_train, y_train) # training set in x, y axis |
- Polynomial Kernel: It represents the similarity of vectors in the training set of data in a feature space over polynomials of the original variables used in the kernel.
Polynomial Kernel Graph
Code:
python3
from sklearn.svm import SVCclassifier = SVC(kernel ='poly', degree = 4)classifier.fit(x_train, y_train) # training set in x, y axis |
- Linear Kernel: used when data is linearly separable.
Code:
python3
from sklearn.svm import SVCclassifier = SVC(kernel ='linear')classifier.fit(x_train, y_train) # training set in x, y axis |
