Vector Quantization

Vector Quantization (VQ) is a method that exploits unsupervised learning in order to perform a lossy compression of a sample x_i ∈ ℜ^N (for simplicity, we are supposing the multi-dimensional samples are flattened) or an entire dataset X. The main idea is to find a codebook Q with a number of entries C << N and associate each element with an entry q_i ∈ Q. In the case of a single sample, each entry will represent one or more groups of features (for example, it can be the mean), therefore, the process can be described as a transformation T whose general representation is:

The codebook is defined as Q = (q₁, q₂, ..., q_C). Hence, given a synthetic dataset made up of a group of feature aggregates (for example, a group of two consecutive elements), VQ associates a single codebook entry:

As the input sample is represented using a combination...