What is the kernel function in SVM

This article mainly shows you "what is the kernel function in SVM", which is easy to understand and clear. I hope it can help you solve your doubts. Let me lead you to study and learn this article "what is the kernel function in SVM".

First of all, when we optimize the SVM, we use the dual optimization of quadratic programming. I remember the first time I thought about why I wanted to solve the dual problem. Later, I also consulted a teacher who explained it to me. If we don't introduce the dual problem, how can we use the kernel function later?

What on earth is the kernel function?

If there is an Input

We say it has n features, and here we call them attribute, not feature. But we don't want to use these features alone, I also want to use features such as

Such features, then we also need to do feature mapping, here

We call it feature, and then we replace it every place we need to use x, using our mapped features.

In our formula, the dot product is used to represent the I th and j th of the sample points, respectively. If we do this mapping, we realize the feature mapping, that is, we use it to replace. But this is not very efficient. Using a small technique, we define a function.

To represent the result of dot product of features after our attributes has done feature mapping. If we find such a function, then we can directly use attributes to calculate the result after our mapping, that is, we can not directly carry out feature mapping, but directly bring attribute into our function to get the result of dot product of features after mapping. In this way, the amount of computation is much smaller, and the complexity of the algorithm is also reduced.

With the above groundwork, we only need to find such a function, which we call a kernel function. When we find a kernel function, if we can determine that our kernel function is correct and meet our requirements, it will become a problem that we have to solve now.

At this time, we define the kernel matrix KJI, and our decision is based on this matrix. Through the properties of the dot product, we know that =, so we have, so our matrix is a symmetric matrix, and we can prove that the matrix is positive semidefinite. So if we want to determine whether a function is a correct kernel function, we only need to prove that the corresponding kernel matrix is positive semidefinite!

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