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Digital Object Identifier 10.1109/MSP.2013.2288990

Date of publication: 12 February 2015

any classes of data are composed as constructive combinations of parts. By constructive combi-

nation, 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 non-

negative 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.

Although the notion of purely constructive composition most obviously applies to nonsignal data such as

counts of populations, compositional models have frequently been employed to explain other forms of data as

well [1]. During the last few years, such models have provided new paradigms to solve old standing audio pro-

cessing problems, e.g., blind and supervised source separation [2], [3] and robust recognition [4]. Therefore, the

models have been used as parts of audio processing systems to advance the state of the art on many problems

that deal with audio data consisting of multiple sources, e.g., on the analysis of polyphonic music [5] and recog-

nition of noisy speech [6]. A significant reason to study these methods is not only their inherent robustness but

[

Tuomas Virtanen, Jort F. Gemmeke, Bhiksha Raj, and Paris Smaragdis

]

[

Uncovering the structure of sound mixtures

]

COMPOSITIONAL

MODELS

for Audio Processing

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