Exploring Hierarchical Concepts: Theoretical and Application Comparisons

Carlo Cavicchia, Maurizio Vichi*, Giorgia Zaccaria

*Corresponding author for this work

Research output: Chapter/Conference proceedingChapterAcademic


Phenomena are usually multidimensional and their complexity cannot be directly explored via observable variables. For this reason, a hierarchical structure of nested latent concepts representing different levels of abstraction of the phenomenon under study may be considered. In this paper, we provide a comparison between a procedure based on hierarchical clustering methods and a novelty model recently proposed, called Ultrametric Correlation Matrix (UCM) model. The latter aims at reconstructing the data correlation matrix via an ultrametric correlation matrix and supplies a parsimonious representation of multidimensional phenomena through a partition of the observable variables defining a reduced number of latent concepts. Moreover, the UCM model highlights two main features related to concepts: the correlation among concepts and the internal consistency of a concept. The performances of the UCM model and the procedure based on hierarchical clustering methods are illustrated by an application to the Holzinger data set which represents a real demonstration of a hierarchical factorial structure. The evaluation of the different methodological approaches—the UCM model and the procedure based on hierarchical clustering methods—is provided in terms of classification of variables and goodness of fit, other than of their suitability to analyse bottom-up latent structures of variables.
Original languageEnglish
Title of host publicationAdvanced Studies in Behaviormetrics and Data Science: Essays in Honor of Akinori Okada
Editors Imaizumi, T. and Nakayama, A. and Yokoyama, S.
Place of PublicationSingapore
PublisherSpringer Singapore
ISBN (Print)9789811527005
Publication statusPublished - 2020
Externally publishedYes

Bibliographical note



Dive into the research topics of 'Exploring Hierarchical Concepts: Theoretical and Application Comparisons'. Together they form a unique fingerprint.

Cite this