Archetypal analysis with missing data: see all samples by looking at a few based on extreme profiles
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadata
Title
Archetypal analysis with missing data: see all samples by looking at a few based on extreme profilesDate
2019-05-13Publisher
American Statistical Association; Taylor & FrancisBibliographic citation
Irene Epifanio, M. Victoria Ibáñez & Amelia Simó (2020) Archetypal Analysis With Missing Data: See All Samples by Looking at a Few Based on Extreme Profiles, The American Statistician, 74:2, 169-183, DOI: 10.1080/00031305.2018.1545700Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/submittedVersionSubject
Abstract
In this paper we propose several methodologies for handling missing or incomplete data in Archetype analysis (AA) and Archetypoid analysis (ADA). AA seeks to find archetypes, which are convex combinations of data ... [+]
In this paper we propose several methodologies for handling missing or incomplete data in Archetype analysis (AA) and Archetypoid analysis (ADA). AA seeks to find archetypes, which are convex combinations of data points, and to approximate the samples as mixtures of those archetypes. In ADA, the representative archetypal data belong to the sample, i.e. they are actual data points. With the proposed procedures, missing data are not discarded or previously filled by imputation and the theoretical properties regarding location of archetypes are guaranteed, unlike the previous approaches. The new procedures adapt the AA algorithm either by considering the missing values in the computation of the solution or by skipping them. In the first case, the solutions of previous approaches are modified in order to fulfill the theory and a new procedure is proposed, where the missing values are updated by the fitted values. In this second case, the procedure is based on the estimation of dissimilarities between samples and the projection of these dissimilarities in a new space, where AA or ADA is applied, and those results are used to provide a solution in the original space. A comparative analysis is carried out in a simulation study, with favorable results. The methodology is also applied to two real data sets: a well-known climate data set and a global development data set. We illustrate how these unsupervised methodologies allow complex data to be understood, even by non-experts. [-]
Investigation project
Spanish Ministry of Ciencia, Innovacin y Universidades (AEI/FEDER, EU) (grant DPI2017-87333-R) ; Universitat Jaume I (UJI-B2017-13 ).Rights
© 2018 Taylor & Francis.
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info:eu-repo/semantics/openAccess
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
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- MAT_Articles [751]