I am confused by 3 figures shown in https://bioconductor.org/packages/release/bioc/vignettes/SomaticSignatures/inst/doc/SomaticSignatures-vignette.html.)
Firstly, how to define the contribution of motif to each mutational signature? What is the meaning of contribution be 1,2 3 or 4? 
Secondly, how to define the contribution of mutational signatures to each sample or study? Why the sum of signature contribution is not 1 or near to 1? 

Hi Zzsu

Your question is a bit open-ended, so the best I can say at this point is to recommend having a look at the accompanying paper https://academic.oup.com/bioinformatics/article-lookup/doi/10.1093/bioinformatics/btv408 and perhaps you'll also benefit from familiarizing yourself with matrix decomposition (SVD, PCA) with a linear algebra textbook. If you have questions about specific normalization or scaling choices made by a certain function in the package, the first step could be having a look at the manual page and indeed the (simple) source code of the function. The second could be to bring back that question to this forum and report (or refer to) a self-contained piece of code,  your explanation of what you would expect to get, and how this differs from what you get.

Kind regards

Wolfgang