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 r c. Each horizontal line represents a component that maintains its identity as r c is increased. In our analysis, we select the two gene groups C 1′ and C 2′ at r c ≈ 0.56, just prior to their merging. C 1′ and C 2′ 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 C 1′ and C 2′. The patient samples are bisected at r c ≈ 0.34 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.