Data Analysis in Metric Spaces Through Metric Observables
Washington Mio, Florida State University
We discuss ways of probing the shape of data in metric spaces using metric observables (1-Lipschitz functions). This leads to a dimension reduction, data visualization, and statistical analysis technique that we call Principal Observable Analysis. We also discuss the construction of robust data summaries associated with such metric observables in the form of filtered merge trees, Reeb graphs, and Leray-Reeb pre-cosheaves.