ABSTRACT

Compositional data (CoDa) quantitatively describe the components of some whole and these components are usually termed parts. According to the experimental fi eld, CoDa appear as vectors of percentages, parts per unit, parts per million, or other non-closed units such as molar concentrations or absolute frequencies. The units used are irrelevant, because the total sum of the vector is not informative, i.e., the information is relative rather than absolute, and lies in the ratios of the parts. For example, in Archeometry the total weight of a material sample is irrelevant when the aim is to analyze the chemical composition of an artifact. Formally, CoDa are considered to be equivalence classes. They thus embrace scale invariance and the sample space of CoDa, the simplex, is SD=൛x∈R+D: ∑ xjDj=1 = kൟ, where the value of the constant k is irrelevant-a popular choice is k = 1-, and D is the number of parts.