What is kernel trick and how it is useful explain the technique where used the kernel trick?
A Kernel Trick is a simple method where a Non Linear data is projected onto a higher dimension space so as to make it easier to classify the data where it could be linearly divided by a plane. This is mathematically achieved by Lagrangian formula using Lagrangian multipliers. (
Why does kernel trick work?
This is when the kernel trick comes in. It allows us to operate in the original feature space without computing the coordinates of the data in a higher dimensional space. In essence, what the kernel trick does for us is to offer a more efficient and less expensive way to transform data into higher dimensions.
Which is an example of the kernel trick?
However, when there are more and more dimensions, computations within that space become more and more expensive. This is when the kernel trick comes in. It allows us to operate in the original feature space without computing the coordinates of the data in a higher dimensional space. Let’s look at an example:
How is the kernel function used in training?
The kernel function has a special property that makes it particularly useful in training support vector models, and the use of this property in optimizing non-linear support vector classifiers is often called the kernel trick.
Why is the polynomial kernel trick so important?
“Intuitively, the polynomial kernel looks not only at the given features of input samples to determine their similarity, but also combinations of these” ( Wikipedia ), just like the example above. With n original features and d degrees of polynomial, the polynomial kernel yields n^d expanded features.
What is the property of the kernel function?
This kernel function has a special mathematical property. The kernel function acts as a modified dot product. We have: Our kernel function accepts inputs in the original lower dimensional space and returns the dot product of the transformed vectors in the higher dimensional space.