How to select landmarks of Kernel to run SVM Objective
Clarify how to choose the kernel reference points (landmarks) to identify the non-linear boundary. 
 
Background
Going through SVM at Coursera ML - Support Vector Machine  and trying to understand how to choose the landmarks to measure the distances to feed into the Gaussian Kernel.
It says "put the landmarks in the exact same locations as all the training examples". 


Question
Not clear why "the exact same locations of all the training data". 


*

*Why using all the data?  Number of features M and the number of data N is different and I suppose M << N. Then should we choose M number of data to use landmarks? 

*Why not considering if a data to use as a landmark is classified positive or negative? 
I believe we would like to distinguish positive data (higher Gaussian probability), then why use the negative data as well as the landmarks?  In the YouTube SVM with polynomial kernel visualization example (although it does not use Gaussian), the landmarks should be those that represent red points?

 A: M is the number of data points, not the number of features.  So we take all our (training) data, and for each (xi,yi), we get a landmark.
Notice that in the combined minimisation term, each fi is combined with its matching yi, so the minimisation takes account of which landmarks should be positive and which should be negative.
In the video each red dot AND each blue dot should be a landmark.
A: Obviously very late, but as Andrew's answer mentions, each $f^{(i)}$ is paired with the same label as $x^{(i)}$. That is, if $x^{(i)}$ is paired with a corresponding label of $1$, then $f^{(i)}$ will also be paired with $1$. For this reason, if we only utilize the features $x^{(i)}$ with corresponding labels of $1$ (i.e. positive features), we'd end up with a transformed dataset in which each of the features $f^{(i)}$ have corresponding label of $1$. Training an SVM on this transformed dataset would therefore yield an SVM that could constantly predict $1$, and obtain a cost of $0$ each time, which obviously isn't very helpful at all.
This is all to say we need to pick both positive and negative feature as landmarks, otherwise we could end up with a transformed dataset so skewed that it becomes impossible to train an SVM with a reasonable test set performance on said transformed dataset.
Hope this helps.
