So, initially when I was using CTW the problem was with VQ, in particular, independence of the quantization from the inference in the Markovian model. I solved that using HMMs so that the quantization is learned simultaneously with the structure.

Now it occurs to me that I don't have a clear cut way of extracting "parts" from the signals, even if in the form of subparts of the signal. I suppose now I can revisit that idea and use compression to extract the most commonly used subparts of a repertoire.