Dimensionality Reduction of Compositional Data with Structural Zeros: A Case Study

In this paper, we introduce the issue of how Principal Component Analysis (PCA) can be performed on compositional datasets with structural zeros. Compositional data describe parts of a whole, and they are characterized by the fact that the relevant information is in the ratios between the parts and not in their absolute values or in their sum. They are usually represented by vectors of proportions since their sum is constant. It is not easy to tackle structural zeros in the compositional framework since, by definition, all the parts of a composition must be strictly positive. We show through an application on a dataset regarding a large number of US mines the issues arising, and we provide some indications that can be followed for facing such a situation.