Recent advances in sequencing technologies have enabled the production of 
massive amounts of data on somatic mutations from cancer genomes. These data 
have led to the detection of characteristic patterns of somatic mutations or 
"mutation signatures" at an unprecedented resolution, with the potential for new 
insights into the causes and mechanisms of tumorigenesis. Here we present new 
methods for modelling, identifying and visualizing such mutation signatures. Our 
methods greatly simplify mutation signature models compared with existing 
approaches, reducing the number of parameters by orders of magnitude even while 
increasing the contextual factors (e.g. the number of flanking bases) that are 
accounted for. This improves both sensitivity and robustness of inferred 
signatures. We also provide a new intuitive way to visualize the signatures, 
analogous to the use of sequence logos to visualize transcription factor binding 
sites. We illustrate our new method on somatic mutation data from urothelial 
carcinoma of the upper urinary tract, and a larger dataset from 30 diverse 
cancer types. The results illustrate several important features of our methods, 
including the ability of our new visualization tool to clearly highlight the key 
features of each signature, the improved robustness of signature inferences from 
small sample sizes, and more detailed inference of signature characteristics 
such as strand biases and sequence context effects at the base two positions 5' 
to the mutated site. The overall framework of our work is based on probabilistic 
models that are closely connected with "mixed-membership models" which are 
widely used in population genetic admixture analysis, and in machine learning 
for document clustering. We argue that recognizing these relationships should 
help improve understanding of mutation signature extraction problems, and 
suggests ways to further improve the statistical methods. Our methods are 
implemented in an R package pmsignature 
(https://github.com/friend1ws/pmsignature) and a web application available at 
https://friend1ws.shinyapps.io/pmsignature_shiny/.