Ultrametric Component Analysis with Application to Analysis of Text and of Emotion
This work provides a framework for analyzing ultrametric structures in data, which is incremental as it builds on existing hierarchical clustering methods for specific domains like text and emotion quantification.
The paper tackles the problem of identifying ultrametric components in metric-endowed datasets by developing a novel consensus of hierarchical clusterings to visualize and interpret locally ultrametric relationships, with applications in text and emotion analysis.
We review the theory and practice of determining what parts of a data set are ultrametric. It is assumed that the data set, to begin with, is endowed with a metric, and we include discussion of how this can be brought about if a dissimilarity, only, holds. The basis for part of the metric-endowed data set being ultrametric is to consider triplets of the observables (vectors). We develop a novel consensus of hierarchical clusterings. We do this in order to have a framework (including visualization and supporting interpretation) for the parts of the data that are determined to be ultrametric. Furthermore a major objective is to determine locally ultrametric relationships as opposed to non-local ultrametric relationships. As part of this work, we also study a particular property of our ultrametricity coefficient, namely, it being a function of the difference of angles of the base angles of the isosceles triangle. This work is completed by a review of related work, on consensus hierarchies, and of a major new application, namely quantifying and interpreting the emotional content of narrative.