Cancer Fingerprints by Topological Data Analysis

Topological data analysis has arisen has a promising tool to extract information on the structure of a wide variety of datasets. We analyze here its potential in two types of cancer studies. First, we compare times series of images from simulations of metastatic invasion in epithelial tissues. Calculating bottleneck distances of persistent diagrams we can characterize and classify the advancing interfaces of cellular aggregates. Second, we compare mRNA expression values for genes involved in cell cycles extracted from pancreas cancer tissue. We discuss how persistence information from different distances can provide insight on patient/gene clusters.