Compositional models for audio processing: Uncovering the structure of sound mixtures

Many classes of data are composed as constructive combinations of parts. By constructive combination, we mean additive combination that does 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. To characterize such data, various mathematical models have been developed in the literature. These models, in conformance with the nature of the data, represent them as nonnegative linear combinations of parts, which themselves are also nonnegative to ensure that such a combination does not result in subtraction or diminishment. We will refer to such models as compositional models.