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# Types of Kernels in Machine Learning

## Solving a non-linear problem using the linear function

In this article, we will talk about the types of kernels used in machine learning to separate non-linear problems data using a linear classifier. The raw data need extra care to get insights and representation from it, the features in the data can be in any pattern and we need to search for the relation between them.

The pattern analysis and relation can be in clusters, correlations, classifications, rankings, etc.

**Kernel Trick:** The study of different kernels uses a kernel function that works in high dimensional space without considering the coordinates of the data. So, this type of process/approach is computationally cheaper and effective.

Different Kernels to be covered:

`1. Linear Kernel`

2. Polynomial Kernel

3. Sigmoid Kernel

4. RBF Kernel

5. Laplacian Kernel

6. Chi-squared Kernel

Linear Kernel

As the name suggests, the kernel separates the data linearly as it is the one-dimensional kernel. Every beginner starts with this simple kernel that is mostly the default value in the algorithm.

The good point of a linear kernel is fast as compared to other kernels because in the linear kernel we need only regularization parameter and in other kernels, we need the addition of the `y`

parameter to performing the grid search.

Equation of Linear Kernel shown below:

Where,

x and y = input column vectors

The `degree=1`

and `coef0=0`

if the coef is zero then the kernel is homogeneous means it maps the data in a compact linear representation.

Polynomial Kernel

As the name suggests, this kernel deals with the degree/order of the features. The relationship between features is not linear but rather a curve, due to this the linear kernel is not suited to get its maximum result because the residue will be more between observed and predicted value.

The working function of this kernel is less effective as compared to other kernels.

Equation of Polynomial Kernel shown below:

Where,

x and y = input column vectors and d = kernel degree

Sigmoid Kernel

This kernel is mostly used in neural networks or perceptron in machine learning. To classify the classes in the data it works as an activation function. The curve in this kernel is also called the cumulative distribution function that goes from 0 to 1.

Many people still confuse about the logit function, the logit function is the inverse of the sigmoid function.

Equation of sigmoid Kernel shown below:

Where,

x and y = input column vectors, ϒ = Slope, and C0 = intercept

RBF Kernel

The most using kernel in the machine learning algorithm to classify the data without knowing the data types and try to separate the classes smoothly. The full form of RBF is the radial basis kernel.

The introduction of RBF in the machine learning kernel is because the other kernels are not trying to scale well on a huge number of input features.

Equation of RBF Kernel shown below:

Where,

x and y = input column vectors, ϒ = ϒ = σ^2, kernel of variance.

Laplacian Kernel

The laplacian kernel is from the family of RBF kernel and it can be used in noiseless data. It is very less affected by the changes in the data and also it has some similar features with the exponential kernel, as we will discuss later in this article.

The application of this kernel is mainly in image processing to detect edges of the objects by the name of Laplacian over Gaussian Filter (LoG).

Equation of Laplacian Kernel shown below:

Where,

x and y = input column vectors, ||x-y||1 = Manhattan distance metric

Chi-squared Kernel

This type of kernel is useful in non-linear data, it looks like an intersection kernel that has worked on the histogram of visual words data. The speed of this kernel is slow and sometimes does not work on sparse data.

The data should be non-zero and positive to have a good result with this kernel and mainly use in computer vision applications.

Equation of Chi-squared Kernel shown below:

Conclusion:

This is a basic type of kernel that is mostly used in the machine learning algorithm.

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