From Data to the Physics Using Ultrametrics: New Results in High Dimensional Data Analysis

We begin with pervasive ultrametricity due to high dimensionality and/or spatial sparsity. How extent or degree of ultrametricity can be quantified leads us to the discussion of varied practical cases when ultrametricity can be partially or locally present in data. We show how the ultrametricity can be assessed in text or document collections, in time series signals, and in other areas. We conclude with a discussion of ultrametricity in astrophysics, relating to observational cosmology.