Archetypal Analysis With Missing Data: See All Samples by Looking at a Few Based on Extreme Profiles
| Autor: | Irene Epifanio, M. Victoria Ibáñez, Amelia Simó |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
multidimensional scaling
Statistics and Probability partial distance strategy Incomplete dataset Theoretical computer science incomplete data set ComputingMilieux_THECOMPUTINGPROFESSION Computer science General Mathematics Missing data archetype analysis TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Archetypal analysis Multidimensional scaling Statistics Probability and Uncertainty Archetype |
| Zdroj: | AMERICAN STATISTICIAN r-FISABIO: Repositorio Institucional de Producción Científica Fundación para el Fomento de la Investigación Sanitaria y Biomédica de la Comunitat Valenciana (FISABIO) Repositori Universitat Jaume I Universitat Jaume I r-FISABIO. Repositorio Institucional de Producción Científica instname |
| ISSN: | 1537-2731 0003-1305 |
| Popis: | In this article, 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, that is, 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 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 datasets: a well-known climate dataset and a global development dataset. We illustrate how these unsupervised methodologies allow complex data to be understood, even by nonexperts. for this article are available online. |
| Databáze: | OpenAIRE |
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