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Identifying subgroups and properties of cancer biopsy samples is a crucialstep towards obtaining precise diagnoses and being able to perform personalizedtreatment of cancer patients. Recent data collections provide a comprehensivecharacterization of cancer cell data, including genetic data on copy numberalterations (CNAs). We explore the potential to capture information containedin cancer genomic information using a novel topology-based approach thatencodes each cancer sample as a persistence diagram of topological features,i.e., high-dimensional voids represented in the data. We find that thistechnique has the potential to extract meaningful low-dimensionalrepresentations in cancer somatic genetic data and demonstrate the viability ofsome applications on finding substructures in cancer data as well as comparingsimilarity of cancer types.

Topological Data Analysis of copy number alterations in cancer