A Robust Clustering Method Using Compositional Data Restrictions: Studying Wood Properties in the Reforestation of Portugal

Abstract

Classification of multivariate observations while preserving the data’s natural restriction is a challenge. Special properties such as identifiability, interpretability, and others need to be cared for to build a new approach. To avoid these complications, many transformation algorithms have been developed to use traditional models.In this context, the aim of this work is to propose a robust probabilistic distance algorithm to classify compositional data. Based on the probabilistic distance (PD) clustering approach, the proposal identifies clusters minimizing a joint distance function, JDF, which is part of a dissimilarity measure. This measure combines the PD clustering approach with the density of the Dirichlet distribution. This procedure allows us to create clusters, and define the number of clusters by accommodating the data’s natural data compositional restriction.This work was motivated by the forestry area in the restoration context.The composition dataset of the populations of Pinus nigra was analyzed via the proposed robust probabilistic distance clustering algorithm. The proposed method allows us to classify the new physical, chemical, and mechanical P. nigra’ properties into clusters. The main results identify compositional clusters which provide support for wider areas’ recognition. In addition, the results can be used in decisions to spread sustainable forest management