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Comparison of Methods to Display Principal Component Analysis, Focusing on Biplots and the Selection of Biplot Axes
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Author(s): Carla Barbosa (REQUINTE-LAQV, Instituto Politécnico de Viana do Castelo, Portugal), M. Rui Alves (REQUINTE-LAQV, Instituto Politécnico de Viana do Castelo, Portugal)and Beatriz Oliveira (REQUINTE-LAQV, Faculdade de Farmácia, Universidade do Porto, Portugal)
Copyright: 2016
Pages: 44
Source title:
Handbook of Research on Computational Simulation and Modeling in Engineering
Source Author(s)/Editor(s): Francisco Miranda (Instituto Politécnico de Viana do Castelo and CIDMA of University of Aveiro, Portugal)and Carlos Abreu (Instituto Politécnico de Viana do Castelo, Portugal)
DOI: 10.4018/978-1-4666-8823-0.ch010
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Abstract
Principal components analysis (PCA) is probably the most important multivariate statistical technique, being used to model complex problems or just for data mining, in almost all areas of science. Although being well known by researchers and available in most statistical packages, it is often misunderstood and poses problems when applied by inexperienced users. A biplot is a way of concentrating all information related to sample units and variables in a single display, in an attempt to help interpretations and avoid overestimations. This chapter covers the main mathematical aspects of PCA, as well as the form and covariance biplots developed by Gabriel and the predictive and interpolative biplots devised by Gower and coworkers. New developments are also presented, involving techniques to automate the production of biplots, with a controlled output in terms of axes predictivities and interpolative accuracies, supported by the AutoBiplot.PCA function developed in R. A practical case is used for illustrations and discussions.
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