Mutational signature analysis is an essential part of the cancer genome analysis toolkit. Conventionally, mutational signature analysis extracts patterns of different mutation types across many cancer genomes. Here we present TensorSignatures, an algorithm to learn mutational signatures jointly across all variant categories and their genomic context. The analysis of 2,778 primary and 3,824 metastatic cancer genomes of the PCAWG consortium and the HMF cohort shows that practically all signatures operate dynamically in response to various genomic and epigenomic states. The analysis pins differential spectra of UV mutagenesis found in active and inactive chromatin to global genome nucleotide excision repair. TensorSignatures accurately characterises transcription-associated mutagenesis, which is detected in 7 different cancer types. The analysis also unmasks replication- and double strand break repair-driven APOBEC mutagenesis, which manifests with differential numbers and length of mutation clusters indicating a differential processivity of the two triggers. As a fourth example, TensorSignatures detects a signature of somatic hypermutation generating highly clustered variants around the transcription start sites of active genes in lymphoid leukaemia, distinct from a more general and less clustered signature of Polη-driven translesion synthesis found in a broad range of cancer types. ### Competing Interest Statement The authors have declared no competing interest.
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