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The ultrametric correlation matrix for modelling hierarchical latent concepts

Author

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  • Carlo Cavicchia

    (University of Rome La Sapienza)

  • Maurizio Vichi

    (University of Rome La Sapienza)

  • Giorgia Zaccaria

    (University of Rome La Sapienza)

Abstract

Many relevant multidimensional phenomena are defined by nested latent concepts, which can be represented by a tree-structure supposing a hierarchical relationship among manifest variables. The root of the tree is a general concept which includes more specific ones. The aim of the paper is to reconstruct an observed data correlation matrix of manifest variables through an ultrametric correlation matrix which is able to pinpoint the hierarchical nature of the phenomenon under study. With this scope, we introduce a novel model which detects consistent latent concepts and their relationships starting from the observed correlation matrix.

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  • Carlo Cavicchia & Maurizio Vichi & Giorgia Zaccaria, 2020. "The ultrametric correlation matrix for modelling hierarchical latent concepts," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(4), pages 837-853, December.
    • Handle: RePEc:spr:advdac:v:14:y:2020:i:4:d:10.1007_s11634-020-00400-z
    DOI: 10.1007/s11634-020-00400-z
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    References listed on IDEAS

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    Cited by:

    1. Adelaide Freitas & Eloísa Macedo & Maurizio Vichi, 2021. "An empirical comparison of two approaches for CDPCA in high-dimensional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 1007-1031, September.
    2. Carlo Cavicchia & Maurizio Vichi & Giorgia Zaccaria, 2023. "Hierarchical disjoint principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 537-574, September.

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