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Unmixing Compositional data with Bayesian Techniques

A general problem in compositional data analysis is the unmixing of a composition into aseries of pure endmembers. In its most complex version, one does neither know the compositionof these endmembers, nor their relative contribution to each observed composition. The problemis particularly cumbersome if the number of endmembers is larger than the number of observedcomponents. This contribution proposes a possible solution of this under-determined problem.The proposed method starts assuming that the endmember composition is known. Then, ageometric characterization of the problem allows to find the set of possible endmember proportionscompatible with the observed composition. Within this set any solution may be valid, but someare more likely than other. To use this idea and choose the “most likely” solution in each case,the problem can be tackled with Bayesian Markov-Chain Monte-Carlo techniques. Finally, oncewe are familiar with MCMC, it is quite straightforward to allow the endmember compositions torandomly vary, and use the same MCMC to estimate the endmember composition most compatiblewith the studied data

Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada

Other contributions: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Author: Tolosana Delgado, Raimon
Abstract: A general problem in compositional data analysis is the unmixing of a composition into aseries of pure endmembers. In its most complex version, one does neither know the compositionof these endmembers, nor their relative contribution to each observed composition. The problemis particularly cumbersome if the number of endmembers is larger than the number of observedcomponents. This contribution proposes a possible solution of this under-determined problem.The proposed method starts assuming that the endmember composition is known. Then, ageometric characterization of the problem allows to find the set of possible endmember proportionscompatible with the observed composition. Within this set any solution may be valid, but someare more likely than other. To use this idea and choose the “most likely” solution in each case,the problem can be tackled with Bayesian Markov-Chain Monte-Carlo techniques. Finally, oncewe are familiar with MCMC, it is quite straightforward to allow the endmember compositions torandomly vary, and use the same MCMC to estimate the endmember composition most compatiblewith the studied data
Document access: http://hdl.handle.net/2072/273439
Language: eng
Publisher: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Rights: Tots els drets reservats
Subject: Anàlisi multivariable -- Congressos
Multivariate analysis -- Congresses
Estadística matemàtica -- Congressos
Mathematical statistics -- Congresses
Estadística bayesiana -- Congressos
Bayesian statistical decision theory -- Congresses
Title: Unmixing Compositional data with Bayesian Techniques
Type: info:eu-repo/semantics/conferenceObject
Repository: Recercat

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