Major Kernel Functions in Support Vector Machine (SVM)

Last Updated : 07 Feb, 2022

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 :
$K (\bar{x}) = 1, if ||\bar{x}|| <= 1$
$K (\bar{x}) = 0, Otherwise$
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.

$K (x, y) = e ^ - (\frac{||x - y||^2} {2 \sigma^2})$

Gaussian Kernel Radial Basis Function (RBF): Same as above kernel function, adding radial basis method to improve the transformation.

$K (x, y) = e ^ - (\gamma{||x - y||^2})$
$K (x, x1) + K (x, x2) (Simplified - Formula)$
$K (x, x1) + K (x, x2) > 0 (Green)$
$K (x, x1) + K (x, x2) = 0 (Red)$

Gaussian Kernel Graph

Code:

python3

from sklearn.svm import SVC
classifier = SVC(kernel ='rbf', random_state = 0)
 # training set in x, y axis
classifier.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.

$K (x, y) = tanh (\gamma.{x^T y}+{r})$

Sigmoid Kernel Graph

Code:

python3

from sklearn.svm import SVC
classifier = 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.

$K (x, y) = tanh (\gamma.{x^T y}+{r})^d, \gamma>0$

Polynomial Kernel Graph

Code:

python3

from sklearn.svm import SVC
classifier = 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 SVC
classifier = SVC(kernel ='linear')
classifier.fit(x_train, y_train) # training set in x, y axis

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