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

• 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
• ISSN: 0888-613X; 1873-4731
• DOI: 10.1016/j.ijar.2015.03.004

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.