Assigning relative variable importance weights in vine mixture clustering

Determine a principled methodology to assign relative weights (importance) to variables within vine copula mixture models used for unsupervised clustering of deprivation indicators and for constructing the proposed probabilistic cluster-driven deprivation ranking, beyond the current leave-one-variable-out approach based on changes in the Bayesian Information Criterion.

Background

The paper introduces a vine copula mixture framework to cluster Scottish zones based on 21 deprivation indicators and proposes a probabilistic cluster-driven ranking derived from posterior cluster membership probabilities. Assessing variable importance in this unsupervised setting is addressed via a leave-one-variable-out strategy that refits the mixture model without each indicator and measures the change in BIC.

The authors note limitations of this approach, including computational intensity and the fact that it does not consider dependence among multiple variables. They explicitly state that determining how to assign relative weights (importance) of variables remains for future research, highlighting an unresolved methodological question relevant to variable importance in vine mixture models and the resulting deprivation ranking.