Summary
In this paper, we propose a new approach to Principal Component Analysis, for interval-valued data. On the basis of the interval arithmetic we show that any continuous interval can be expressed in terms of a midpoint (location) and of a radius (variation). Moving from this result, we propose a well suited factorial analysis, which exploits this characteristic of interval data. Both the location and variation information are represented on maps.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alefeld G, Herzerberger J (1983) Introduction to Interval computation. Academic Press, New York.
Bock HH, Diday E, eds. (1999) Analysis of Symbolic Data. Springr Verlag, Hiedelberg.
Cazes P, Chouakria A, Diday E, Schektman Y (1997) Extension de l’analyse en composantes principales à des données de type intervalle. Revue de Statistique Appliquée XIV (3): 5–24.
Gower JC (1975) Generalized Procrustes analysis. Psychom. 40: 33–51.
Lauro CN, Palumbo F (2000) Principal component analysis of interval data: A symbolic data analysis approach. Comp. Stat. 15 (1): 73–87.
Mardia KV, Kent JT, Bibby JM (1979) Multivariate Analysis. Academic Press, London, pp 416–417.
Neumaier A (1990) Interval methods for systems of Equations. Cambridge University Press, Cambridge.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2003 Springer Japan
About this paper
Cite this paper
Palumbo, F., Lauro, C.N. (2003). A PCA for interval-valued data based on midpoints and radii. In: Yanai, H., Okada, A., Shigemasu, K., Kano, Y., Meulman, J.J. (eds) New Developments in Psychometrics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-66996-8_74
Download citation
DOI: https://doi.org/10.1007/978-4-431-66996-8_74
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-66998-2
Online ISBN: 978-4-431-66996-8
eBook Packages: Springer Book Archive