From a recent paper on Nature Genetics by our collaborator Laura, from the supplemental data I learned that she used Hierarchical Dirichlet Process to extract the signature.

In fact, it is her colleague Nicola Roberts, who first posted the HDP R package in 2015. Nicola also has a vignette on his package using the TCGA data to publish his HDP package.

It is quite interesting but the process is a computational intensive process.