Fig. 2: K-means unsupervised clustering analysis identifies nine tumour metabolic subpopulations.

a Optimisation of the cluster presence threshold from K = 2 to 10 for comparison with clinical endpoint assessed by the Akaike Information Criterion (AIC) of Cox proportional hazards regression models. The AIC values were scaled to 0–1 and visualised as in a heatmap. Cluster numbers of K = 9 and K = 10 show the lowest AIC value at a threshold of 24%, and thus are defined as the optimal number of clusters. All the subsequent analysis was based on K = 9. b Mass spectra and ion distribution maps based on nine subpopulations of metabolites as generated by K-means analysis. K-means image was created by labelling each pixel according to its subpopulation label. c Uniform Manifold Approximation and Projection (UMAP) analysis of nine subpopulations. The points represent samples and are coloured by the tumour subpopulation label of each pixel. d Bar plot of the number of patients contributing to each of the subpopulations.