Fig. 1. A multidimensional tensor factorisation framework to extract mutational signatures.

a Splitting variants by transcriptional and replicational strand, and genomic states creates an array of count matrices, a multidimensional tensor, in which each matrix harbours the mutation counts for each possible combination of genomic states. b TensorSignatures factorises a mutation count tensor (SNVs) into an exposure matrix and signature tensor. Simultaneously, other mutation types (MNVs, indels, SVs), represented as a conventional count matrix are factorised using the same exposure matrix. c The signature tensor has itself a lower dimensional structure, defined by the product of strand-specific signatures, and coefficients reflecting the activity of the mutational process in a given genomic state combination.