Compositional models for audio processing

Many classes of data are composed as constructive combinations of parts. By ”constructive” combination, we mean additive combination that do not result in subtraction or diminishment of any of the parts. We will refer to such data as “compositional” data. Typical examples include population or counts data, where the total count of a population is obtained as the sum of counts of subpopulations. In order to characterize such data, a variety of mathematical models have been developed in the literature which, in conformance with the nature of the data, represent them as non-negative linear combinations of parts which themselves are also non-negative, to ensure that such combination does not result in subtraction or diminishment. We will refer to such models as “compositional” models.