An interval estimator for the unmixing of mixtures with set-based source descriptions

The unmixing of mixtures, i.e., the computation of the proportional contribution of a set of sources to a mixture, is of interest to a multitude of applied research disciplines. We consider an unmixing problem in which a mixture is represented by a point in Rn, and the sources are represented by sub...

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Bibliographic Details
Published in:International journal of approximate reasoning 2015-05, Vol.60, p.71-92
Main Authors: Verwaeren, Jan, Rademaker, Michael, De Baets, Bernard
Format: Article
Language:English
Subjects:
Approximation
Computation
Descriptions
Estimators
Interval estimation
Intervals
Mathematical optimization
Mixtures
Optimization
Reasoning
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Summary:The unmixing of mixtures, i.e., the computation of the proportional contribution of a set of sources to a mixture, is of interest to a multitude of applied research disciplines. We consider an unmixing problem in which a mixture is represented by a point in Rn, and the sources are represented by subsets of Rn. We argue that the proportional contribution of a source of interest to that mixture can naturally be estimated by an interval estimator, as opposed to a more traditional point estimator. An interval estimator is proposed and it is shown that this estimator can be computed efficiently in a variety of cases by solving an optimization problem. •We propose an interval estimator for the proportional contribution of a source (or ingredient) to a mixture.•Sources (or ingredients) can be represented by means of sets.•We present a computationally tractable optimization problem to compute an interval estimate in practice.
ISSN:0888-613X
1873-4731
DOI:10.1016/j.ijar.2015.03.004