What is Mercers condition?

In mathematics, specifically functional analysis, Mercer’s theorem is a representation of a symmetric positive-definite function on a square as a sum of a convergent sequence of product functions.

What are the necessary conditions for a valid kernel function?

The most straight forward test is based on the following: A kernel function is valid if and only if the kernel matrix for any particular set of data points has all non-negative eigenvalues. You can easily test this by taking a reasonably large set of data points and simply checking if it is true.

Why do we use polynomial kernel?

In machine learning, the polynomial kernel is a kernel function commonly used with support vector machines (SVMs) and other kernelized models, that represents the similarity of vectors (training samples) in a feature space over polynomials of the original variables, allowing learning of non-linear models.

What is the purpose of kernel functions in support vector machines?

“Kernel” is used due to set of mathematical functions used in Support Vector Machine provides 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 transformed to a linear equation in a higher number of dimension spaces.

Is polynomial kernel positive definite?

In fact, polynomial kernels are always positive semidefinite for ci ≥ 0 and for positive semidefinite k(x,y).

What is the purpose of the kernel function in kernel SVM?

The kernel functions are used as parameters in the SVM codes. They help to determine the shape of the hyperplane and decision boundary. We can set the value of the kernel parameter in the SVM code. The value can be any type of kernel from linear to polynomial.

What is the benefit of using a polynomial or RBF kernel over a linear kernel?

Decision boundary with a polynomial kernel. The advantage of using the kernelized version is that you can specify the degree to be large, thus increasing the chance that data will become linearly separable in this high-dimensional space, without slowing the model down.

What are benefits of using kernels in SVM *?