  Identifying subgroups and properties of cancer biopsy samples is a crucial
step towards obtaining precise diagnoses and being able to perform personalized
treatment of cancer patients. Recent data collections provide a comprehensive
characterization of cancer cell data, including genetic data on copy number
alterations (CNAs). We explore the potential to capture information contained
in cancer genomic information using a novel topology-based approach that
encodes each cancer sample as a persistence diagram of topological features,
i.e., high-dimensional voids represented in the data. We find that this
technique has the potential to extract meaningful low-dimensional
representations in cancer somatic genetic data and demonstrate the viability of
some applications on finding substructures in cancer data as well as comparing
similarity of cancer types.
