Archetypal analysis: Contributions for estimating boundary cases in multivariate accommodation problem

Computers & Industrial Engineering, Volume 64, Issue 3, March 2013, Pages 757-765.

I. Epifanio, G. Vinué, S. Alemany.

Dept. de Matemàtiques, Universitat Jaume I, Castelló, Spain and

Department of Statistics and O.R., University of Valencia, Valencia, Spain and

Biomechanics Institute of Valencia, Universidad Politécnica de Valencia, Valencia, Spain.




The use of archetypal analysis is proposed in order to determine a set of representative cases that entail a certain percentage of the population, in the accommodation problem. A well-known anthropometric database has been used in order to compare our methodology with the common used PCA-approach, showing the advantages of our methodology: the level of accommodation is reached unlike the PCA approach, no more adjustments are necessary, the user can decide the number of archetypes to consider or leave the selection by a criterion. Unlike PCA, the objective of the archetypal analysis is obtaining extreme individuals, so it is the appropriate statistical technique for solving this type of problem. Archetypes cannot be obtained with PCA even if we consider all the components, as we show in the application.


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Additional Information: 

“Six variables from the 1967 USAF Survey were used for determining boundary cases in order to design aircraft cockpits. After removing the more extreme 5% data, we applied archetypal analysis to get the archetypes (the boundary cases). With our methodology, we obtained seven archetypes (see the figure), one of them could not be extracted by any principal component (PCA is the most common methodology for obtaining the boundary cases). Our methodology effectively considers a certain percentage of the population for accommodation, not as the classical PCA, where the percentage of accommodation is determined without considering all the variability. Consequently, PCA does not ensure to reach the desired level of accommodation. Choosing appropriately the boundary cases for design is really critical, as this can produce a better design that fits the desired percentage of population. In the aircraft cockpit design, this is translated into improving the pilot performance and safety. Archetypes can be easily obtained as the code is free and open.”


Archetypal analysis Contributions for estimating boundary cases in multivariate accommodation problem