Hierarchical relationships among manifest variables can be detected by analyzing their correlation matrix. To pinpoint the hierarchy underlying a multidimensional phenomenon, the Ultrametric Correlation Model (UCM) has been proposed with the aim of reconstructing a nonnegative correlation matrix via an ultrametric one. In this paper, we illustrate the mathematical advantages that a simple structure induced by the ultrametric property entails for the estimation of the UCM parameters in a maximum likelihood framework.
Cavicchia, C., Vichi, M., Zaccaria, G. (2021). A parsimonious parameterization of a nonnegative correlation matrix. In S. Ingrassia, A. Punzo, R. Rocci (a cura di), Book of short papers of the 5th international workshop on models and learning for clustering and classification MBC2 2020, Catania, Italy (pp. 21-26). Ledizioni.
A parsimonious parameterization of a nonnegative correlation matrix
Zaccaria, G
2021
Abstract
Hierarchical relationships among manifest variables can be detected by analyzing their correlation matrix. To pinpoint the hierarchy underlying a multidimensional phenomenon, the Ultrametric Correlation Model (UCM) has been proposed with the aim of reconstructing a nonnegative correlation matrix via an ultrametric one. In this paper, we illustrate the mathematical advantages that a simple structure induced by the ultrametric property entails for the estimation of the UCM parameters in a maximum likelihood framework.
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