A robust topology-based algorithm for gene expression profiling.

Early and accurate diagnoses of cancer can significantly improve the design of personalized therapy and enhance the success of therapeutic interventions. Histopathological approaches, which rely on microscopic examinations of malignant tissue, are not conducive to timely diagnoses. High throughput genomics offers a possible new classification of cancer subtypes. Unfortunately, most clustering algorithms have not been proven sufficiently robust. We propose a novel approach that relies on the use of statistical invariants and persistent homology, one of the most exciting recent developments in topology. It identifies a sufficient but compact set of genes for the analysis as well as a core group of tightly correlated patient samples for each subtype. Partitioning occurs hierarchically and allows for the identification of genetically similar subtypes. We analyzed the gene expression profiles of 202 tumors of the brain cancer glioblastoma multiforme (GBM) given at the Cancer Genome Atlas (TCGA) site. We identify core patient groups associated with the classical, mesenchymal, and proneural subtypes of GBM. In our analysis, the neural subtype consists of several small groups rather than a single component. A subtype prediction model is introduced which partitions tumors in a manner consistent with clustering algorithms but requires the genetic signature of only 59 genes.