The lloyd-max algorithm for scalar quantization chooses points randomly in the begining which causes the problem of local minima and global minima
possibily giving a non optimal solution
So
instead of choosing points randomly in the begining
can we choose them in this way
consider the pdf the r.v.
integrate the pdf till we get 0.5
consider this point as the first boundary point b1
then divide the intervals so obtained further again
in the first interval integrate till cdf is 0.25
consider this to be the second boundary point b2
thus we can acquire as many points as required considering the probabilistic behaviour of the rv
once sufficient number of boundary points are obtained we can the apply the lloyd max algo considering this boundary points
taking the mse and finding the approximation points a1 to an
then working on a1 to an to find the boundary points
the added part would take care that areas which have more probability will have the approximation points closer reducing the mse
hence the drawback mentioned in your notes where points choosen randomly may not be best if probability distributions are considered
can be resolved
