A Robust Topology-Based Algorithm for Gene Expression Profiling

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.

(a)

(b)