Response to the following problem:
In the program trainvq . c the empty cell problem is resolved by replacing the vector with no associated training set vectors with a training set vector from the quantization region with the largest number of vectors. In this problem, we will investigate some possible alternatives. Generate a sequence of pseudorandom numbers with a triangular distribution between 0 and 2. (You can obtain a random number with a triangular distribution by adding two uniformly distributed random numbers.) Design an eight-level, two-dimensional vector quantizer with the initial codebook shown in Table .
(a) Use the trainv q program to generate a codebook with 10,000 random numbers as the training set. Comment on the final codebook you obtain. Plot the elements of the codebook and discuss why they ended up where they did.
(b) Modify the program so that the empty cell vector is replaced with a vector from the quantization region with the largest distortion. Comment on any changes in
the distortion (or lack of change). Is the final codebook different from the one you obtained earlier?
(c) Modify the program so that whenever an empty cell problem arises, a two-level quantizer is designed for the quantization region with the largest number of output points. Comment on any differences in the codebook and distortion from the previous two cases.