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 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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