Abstract
We describe the minimum volume simplex enclosure problem (MVSEP), which is known to be a global optimization problem, and further investigate its multimodality. The problem is a basis for several (unmixing) methods that estimate so-called endmembers and fractional values in a linear mixing model. We describe one of the estimation methods based on MVSEP. We show numerically that using nonlinear optimization local search leads to the estimation results aimed at. This is done using examples, designing instances and comparing the outcomes with a maximum volume enclosing simplex approach which is used frequently in unmixing data.
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The authors gratefully thank the Guest Editors and the Anonymous Reviewers for their outstanding comments and suggestions, which greatly helped us to improve the technical quality and presentation of the manuscript.
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This work has been supported by the European Community Marie Curie Research Training Networks Program (MRTN-CT-2006-035927), Hyperspectral Imaging Network (HYPER-I-NET), the Spanish Ministry of Science and Innovation (TIN2008-01117 and AYA2008-05965-C04-02), Junta de Andalucía (P11-TIC-7176) and Junta de Extremadura (PRI09A110) in part financed by the European Regional Development Fund (ERDF). Eligius Hendrix is a fellow of the Spanish “Ramon y Cajal” program cofinanced by the European Social Fund.
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Hendrix, E.M.T., García, I., Plaza, J. et al. On the minimum volume simplex enclosure problem for estimating a linear mixing model. J Glob Optim 56, 957–970 (2013). https://doi.org/10.1007/s10898-012-9876-5
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DOI: https://doi.org/10.1007/s10898-012-9876-5