Neural gas for vector quantizationpaper explains a technique for symbolizing or quantizing data. Algorithm presents the algorithm in Section 4. An application in EEG data symbolization is presented Application. In the Application it is shown that an n- dimensional data like EEG recordings is vectorized to 1D. But Neural gas is basically an unsupervised clustering algorithm where data can be assigned to more than one cluster.
The definition of Vector Quantization (VQ) is the process of quantizing n-dimensional input vectors to a limited set of n-dimensional output vectors referred to as code-vectors. The set of possible code-vectors is called the codebook. The codebook is usually generated by clustering a given set of training vectors (called training set), the codebook is then used to quantize input vectors.
What I do not understand is that how a multi dimensional data is converted to single dimension as in the Application paper and the module where the symbols are assigned. In the Algorithm, I did not understand what is "reference vector $w_{c_i}$, the set $A$ and Step 3 where it says to order all elements of $A$ according to distance. What is the distance measure here?
Can somebody please explain the algorithm in simple terms how the symbolization is done? Thank you