  This study tackles the efficient estimation of Kullback-Leibler (KL)
Divergence in Dirichlet Mixture Models (DMM), crucial for clustering
compositional data. Despite the significance of DMMs, obtaining an analytically
tractable solution for KL Divergence has proven elusive. Past approaches relied
on computationally demanding Monte Carlo methods, motivating our introduction
of a novel variational approach. Our method offers a closed-form solution,
significantly enhancing computational efficiency for swift model comparisons
and robust estimation evaluations. Validation using real and simulated data
showcases its superior efficiency and accuracy over traditional Monte
Carlo-based methods, opening new avenues for rapid exploration of diverse DMM
models and advancing statistical analyses of compositional data.
