Ultrametric Component Analysis with Application to Analysis of Text and of Emotion

摘要

We review the theory and practice of determining what parts of a data set areultrametric. It is assumed that the data set, to begin with, is endowed with ametric, and we include discussion of how this can be brought about if adissimilarity, only, holds. The basis for part of the metric-endowed data setbeing ultrametric is to consider triplets of the observables (vectors). Wedevelop a novel consensus of hierarchical clusterings. We do this in order tohave a framework (including visualization and supporting interpretation) forthe parts of the data that are determined to be ultrametric. Furthermore amajor objective is to determine locally ultrametric relationships as opposed tonon-local ultrametric relationships. As part of this work, we also study aparticular property of our ultrametricity coefficient, namely, it being afunction of the difference of angles of the base angles of the isoscelestriangle. This work is completed by a review of related work, on consensushierarchies, and of a major new application, namely quantifying andinterpreting the emotional content of narrative.