where wi denotes the weight of each mixture component. The karyotype models Ki are J × Q SCNA probability matrices obtained by clustering arm-level homologous copy-states of modeled copy-profiles using the standard expectation-maximization (EM) algorithm 57 for multinomial mixtures. This calculation identifies groups of disease subtypes with similar genomic copy profiles (Supplementary Fig. 2). Note that copy-states for both homologues of each arm are modeled (J = 78). Karyotype scores for samples with only total copy-ratio data are calculated using convolution of the multinomial probabilities for the two homologous chromosomes.
