Leukemia gene expression results. Scatter plot showing the association between phenotype gene set enrichment p-values and unsupervised gene set enrichment p-values computed using the benchmark cluster-based method (plot a)) and SGSE (plots b) and c)) for the Armstrong et al.  leukemia gene expression data, AML/ALL phenotype, and MSigDB C2 v4.0 gene sets. Phenotype enrichment, unsupervised cluster-based enrichment and spectral gene set enrichment p-values were computed as outlined in Section “Evaluation using MSigDB C2 v4.0 gene sets and Armstrong et al. leukemia gene expression data”. Displayed in each plot is the Spearman correlation coefficient between phenotype and unsupervised gene set enrichment p-values and the positive predictive value of unsupervised gene set enrichment for identifying gene sets that are significantly enriched relative to the phenotype at an α=0.1 (shown by dotted lines). The results from the two different SGSE weighting methods outlined in Section “Combined significance of PCGSE p-values” are shown in plots b) and c) with b) plotting SGSE p-values generated using PC variance weighting and c) plotting SGSE p-values generated using weights defined by the PC variance scaled by the lower-tailed Tracy-Widom p-value for the variance.