# Understanding SVM Kernels

Following Andrew Ng's machine learning course, he explains SVM kernels by manually selecting 3 landmarks and defining 3 gaussian function based on them. Then he says that we are actually defining 3 new features which are $$f_1$$, $$f_2$$ and $$f_3$$.

$$\hskip0.9in$$

And by applying these 3 gaussian functions on every input data: $$x=(x_1,x_2)\to \hat{x}=(f_1(x), f_2(x), f_3(x))$$

it seems that we are mapping our data from $$\mathbb R^2$$ space to a $$\mathbb R^3$$ space. Now our goal is to find a hyperplane in the 3 dimensional space, where our transformed data is linearly separable. Is my understanding correct? If not, how these 3 new features should be interpreted?

$$\hskip1in$$

In some blog posts, i have read that by using a gaussian kernel, we are mapping our data to an infinite dimensional space (where gaussian kernel computes the dot product of transformed input data) which contradicts with my above understandings.

• Thanks, i read the post, but i'm not sure i understand. By using a gaussian kernel $K$, we are implicitly mapping our $\mathbb R^2$ input space to an infinite dimensional space (using a mapping function $\phi(x)$ that $K(x,y)=\phi(x) \cdot \phi(y)$). Then by selecting 3 landmarks $l^{(1)}$, $l^{(2)}$, $l^{(3)}$, we are actually selecting 3 dimensions of that infinite dimensional space. Is that right? Are those dimensions $f_1(x)$, $f_2(x)$ and $f_3(x)$ ? Commented Apr 24, 2020 at 20:52