The wrapper is a lossy representation of the full training spectra that works like a dictionary of templates. What it sacrifices is the minute details of the data manifold, which is sometimes critical for recovering quality audio signals. We are working on some probabilistic topic models with sparsity constraints so as to learn the hyper topics each of which represents only its local neighbors. Those hyper topics play a role in getting manifold preserving quantization of training signals instead of wrappers
and in leading the recovered source spectra to lying on the original data manifold.
See our paper for more detail: "Manifold Preserving Hierarchical Topic Models for Quantization and Approximation (ICML 2013)"