# What is test and what is training data in this SVM formula?

I am studying how to use Gaussian RBF kernels for mapping 2D data to 3D. In this link: Use Gaussian RBF kernel for mapping of 2D data to 3D, @MaxS provides an answer on this topic, but I can't understand this formula:

$$\newcommand{\x}{\mathbf{x}} z(\x) = \sum_{i=1}^n\exp\left\{-\frac{||\x-\x_i||^2}{2\gamma^2}\right\}$$

• If I want to use SVM, is $\x$ the test data?
• Is $n$ number of training data?
• Is $\x_i$ one of training data in this formula?

Yes to 1 and 3. $n$ is the number of support vectors, which is typically less than the number of training instances.

• thanks,can you explain more it for me? do you mean that after we used SVM, we can define z for our new data? and why can not we use all training data? I really appreciate you for your help. – nnp nnp Apr 3 '15 at 18:17
• I search about this and think that because the value of alpha is zero for nsv you said n is number of support vectors,Am I right? – nnp nnp Apr 5 '15 at 7:37
• @nnpnnp yes that is right! – Marc Claesen Apr 5 '15 at 9:15