A least squares approach to Principal Component Analysis for interval valued data

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A least squares approach to Principal Component Analysis for interval valued data

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D'Urso, Perpaolo
Giordani, Paolo ()

Abstract

Principal Component Analysis (PCA) is a well known technique the aim of which is to synthesize huge amounts of numerical data by means of a low number of unobserved variables, called components. In this paper, an extension of PCA to deal with interval valued data is proposed. The method, called Midpoint Radius Principal Component Analysis (MR-PCA) recovers the underlying structure of interval valued data by using both the midpoints (or centers) and the radii (a measure of the interval width) information. In order to analyze how MR-PCA works, the results of a simulation study and two applications on chemical data are proposed.

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Paper provided by University of Molise, Dept. SEGeS in its series Economics & Statistics Discussion Papers with number esdp03013.

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Length: 29 pages
Date of creation: 04 Nov 2003
Date of revision:
Handle: RePEc:mol:ecsdps:esdp03013

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General

This paper has been announced in the following NEP Reports:

NEP-ALL-2003-11-09 (All new papers)
NEP-ECM-2003-11-09 (Econometrics)
NEP-RMG-2003-11-09 (Risk Management)

References listed on IDEAS
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Timmerman, Marieke E. & Kiers, Henk A. L., 2002. "Three-way component analysis with smoothness constraints," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 447-470, September. [Downloadable!] (restricted)
D'Urso, Pierpaolo & Gastaldi, Tommaso, 2000. "A least-squares approach to fuzzy linear regression analysis," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 427-440, October. [Downloadable!] (restricted)
Ledyard Tucker, 1966. "Some mathematical notes on three-mode factor analysis," Psychometrika, Springer, vol. 31(3), pages 279-311, September. [Downloadable!] (restricted)
Giordani, Paolo & Kiers, Henk A. L., 2004. "Principal Component Analysis of symmetric fuzzy data," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 519-548, April. [Downloadable!] (restricted)
Roger Millsap & William Meredith, 1988. "Component analysis in cross-sectional and longitudinal data," Psychometrika, Springer, vol. 53(1), pages 123-134, March. [Downloadable!] (restricted)

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