Non-Euclidean Data Analysis With Metric Statistics

In classical data analysis, the atoms of data are scalars, vectors or functions, where the fact that these are elements of a vector space is fundamental for statistical methodology. The classical approach falls short for data where the data atoms are random objects located in metric spaces for which linear operations are not available. Examples of practical interest are samples of distributions, networks, covariance matrices or trees; these objects reside in spaces that do not possess linear structure, so that even elementary operations such as addition cannot be executed. In this article we showcase applications of some recently developed tools for such data, including measures of location and spread, regression, depth and quantiles.