Changes in the number of copies of certain parts of the genome, known as copy number alterations (CNAs), due to somatic mutation processes are a hallmark of many cancers. This genomic complexity is known to be associated with poorer outcomes for patients but describing its contribution in detail has been difficult. Copy number alterations can affect large regions spanning whole chromosomes or the entire genome itself but can also be localised to only small segments of the genome and no methods exist that allow this multi-scale nature to be quantified. In this paper, we address this using Wave-LSTM, a signal decomposition approach designed to capture the multi-scale structure of complex whole genome copy number profiles. Using wavelet-based source separation in combination with deep learning-based attention mechanisms. We show that Wave-LSTM can be used to derive multi-scale representations from copy number profiles which can be used to decipher sub-clonal structures from single-cell copy number data and to improve survival prediction performance from patient tumour profiles.
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