Multivariate analysis of global-clustering results. Linear discriminant analysis (LDA) was applied to clusters distribution results, used as unique input, rather than using spectral features as traditionally done in the literature. This starts from the hypothesis that the distribution of subcellular features -represented by 17 clusters -can be associated with different leukemia subtypes. The resulting scatter plots, reporting the scores of the first two canonical variables (CVs) for each LDAs, are shown in Fig. , b , and c. The scatter plots including all the calculated CVs are reported in Fig. and S8 for "AMLs+ALLs" and "AMLs", respectively (LDA of "ALLs" produced only 2 CVs, with data already reported in Fig. ). The scalings (also called LDA coefficients or loadings), providing the interpretation about the importance of different clusters in the separation of different cells and subtypes, were calculated for the three LDAs and reported in Fig. . As shown in Fig. and Fig. , representing scores of all nine leukemia subtypes after LDA of "AMLs+ALLs", a certain degree of separation was obtained between different subtypes. Clear maturation and differentiation trends can be also observed (see arrows in Fig. ). More in details, the decrease of CV2 scores (to the bottom side of the scatter plot) describes the maturation trend of leukemia cells: from M0 (undifferentiated leukemia cells, called "blasts") to more mature cells in both the myeloid (i.e., AML M1, M2, M3, M5a and M6) and the lymphoid (i.e., ALL B and T) lineages. Instead, CV1 scores describe the differentiation trend of leukemia cells towards clearly different phenotypes: negative CV1 scores bring to promyelocytes (from AML M1 to M3); positive CV1 scores bring to lymphoblasts (ALLs) and monoblasts (AML M5a). Despite being a supervised method, the fact that LDA provided valuable insights into the ordering of leukemia subtypes by maturation and differentiation status -even though this information was not explicitly provided to the algorithm -demonstrates the validity and robustness of the method, suggesting that LDA of clustering results captured underlying patterns beyond the explicitly labeled class information. The differentiation towards erythroblasts (AML M6) is only marginally described by CV2 scores (close to zero) but this is clearly visible when considering scores of CV3 and CV4 (Fig. ). In parallel, scalings related to CV1 (Fig. ) show the importance of MPO-related clusters (negative CV1 values) and of carotenoids-related clusters (positive CV1 values) in the description of leukemia cell differentiation toward promyelocytes or toward monoblasts, respectively. As confirmation, the confusion matrix produced by the LDA of clustering results (Table , "AMLs+ALLs") shows good classification performances associated with AML M5a and M6 (F 1 -scores of 0.87 and 1, respectively). A certain degree of separation can be seen between M0, M1, M2, and M3 but these are sometime misclassified (F 1 -scores between 0.64 and 0.68; Table ), and this is mainly due to the presence of MPO clusters in these four diseases. ALL B Ph+ and ALL B Ph-are generally misclassified (F 1 -score 0.57 and 0.58, respectively) but ALL T can be partially distinguished from ALL Bs (F 1 -score 0.70, Table ). ALL subtypes are subject to differential diagnoses and misinterpretation also in clinical practice , as distinguishing between ALLs by visual and morphological criteria is not always straightforward.