Kernel Functions for SVM

Kernel functions or Kernel trick can also be regarded as the tuning parameters in an SVM model. They are responsible for removing the computational requirement to achieve the higher dimensional vector space and deal with the non-linear separable data. Here’s our post on the SVM model.

The SVM kernel could be a function that takes low dimensional input space and transforms it into a better dimensional space, i.e., it converts non-separable problems to separable problems. It helps us to deal with non-linear separation problems. Simply put, it does some extremely complex data transformations, then finds out the method to separate the data points based on the target classes you’ve defined. Let us discuss two of the widely used kernel functions.

Types of kernels:

1. Linear kernel:

It is the most basic type of kernel, usually one-dimensional in nature. It proves to be the best function when there are lots of features. The linear kernel is mostly preferred for text classification problems as most of these kinds of classification problems can be linearly separated.

Linear kernel functions are faster than other functions.

Linear Kernel Formula:  F(x, xj) = sum( x.xj)

Here, x, xj represents the data you’re trying to classify.

2. Polynomial kernel:

It is a more generalized representation of the linear kernel. It is not as preferred as other kernel functions as it is less efficient and accurate.

Polynomial Kernel Formula: F(x, xj) = (x.xj+1)d

Here ‘.’ shows the dot product of both the values and d denotes the degree. 

F(x, xj) represents the decision boundary to separate the given classes. 

3. Radial basis function kernel (RBF)/ Gaussian Kernel:

It is one of the most preferred and used kernel functions in SVM. It is usually chosen for non-linear data. It helps to make proper separation when there is no prior knowledge of data.

Gaussian Radial Basis Formula: F(x, xj) = exp(-gamma * ||x – xj||2)

The value of gamma varies from 0 to 1. You have to manually provide the value of gamma in the code. The most preferred value for gamma is 0.1.

There’s more:

Here are a few more references on the SVM kernel:

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