Identifying and exploiting ultrametricity

Abstract

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, and in time series signals. In our presentation we also discussed applications to chemical information retrieval and to astrophysics, in particular observational cosmology.