Kernels or kernel methods (also called Kernel functions) are sets of different types of algorithms that are being used for pattern analysis. They are used to solve a non-linear problem by using a linear classifier. Kernels Methods are employed in SVM (Support Vector Machines) which are used in classification and regression problems. The SVM uses what is called a “Kernel Trick” where the data is transformed and an optimal boundary is found for the possible outputs.
Kernel Function in Machine Learning
In Machine Learning, Kernel us usually used to refer to the kernel trick, a method of using a linear classifier to solve a non-linear problem.
The kernel function is what is applied on each data instance to map the original non-linear observations into a higher-dimensional space in which they become separable.
Kernel Trick allows us to operate in the original feature space without computing the coordinates of the data in a higher dimensional space.
Here we have different types of kernels used in SVM (Support Vector Machine)
1. Liner Kernel
Let us say that we have two vectors with name x1 and Y1, then the linear kernel is defined by the dot product of these two vectors:
K(x1, x2) = x1 . x2
2. Polynomial Kernel
A polynomial kernel is defined by the following equation:
K(x1, x2) = (x1 . x2 + 1)d,
Where,
d is the degree of the polynomial and x1 and x2 are vectors
3. Gaussian Kernel
This kernel is an example of a radial basis function kernel. Below is the equation for this:
The given sigma plays a very important role in the performance of the Gaussian kernel and should neither be overestimated and nor be underestimated, it should be carefully tuned according to the problem.
4. Exponential Kernel
This is in close relation with the previous kernel i.e. the Gaussian kernel with the only difference is – the square of the norm is removed.
The function of the exponential function is:
This is also a radial basis kernel function.
5. Laplacian Kernel
This type of kernel is less prone for changes and is totally equal to previously discussed exponential function kernel, the equation of Laplacian kernel is given as:
6. Hyperbolic or the Sigmoid Kernel
This kernel is used in neural network areas of machine learning. The activation function for the sigmoid kernel is the bipolar sigmoid function. The equation for the hyperbolic kernel function is:
This kernel is very much used and popular among support vector machines.
7. Anova radial basis kernel
This kernel is known to perform very well in multidimensional regression problems just like the Gaussian and Laplacian kernels. This also comes under the category of radial basis kernel.
The equation for Anova kernel is :
There are a lot more types of Kernel Method and we have discussed the mostly used kernels. It purely depends on the type of problem which will decide the kernel function to be used.
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