Figure 3: Using persistent homology for partitioning a set of objects. (a) The barcode on the top panel shows groups of genes of size 5 or more as a function of the cutoff radius . Each horizontal line represents a component that maintains its identity as is increased. In our analysis, we select the two gene groups and at , just prior to their merging. and contain 17 and 20 genes, respectively. (b) The bottom panel shows partitions of 10 or more patient samples computed using the expression levels of members of and . The patient samples are bisected at into two partition of sizes 84 and 76. The first group contains patient samples of the classical and mesenchymal subtypes, while the second contains samples of the proneural subtype.