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

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  • D'Urso, Pierpaolo
  • 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.

Suggested Citation

  • D'Urso, Pierpaolo & Giordani, Paolo, 2003. "A least squares approach to Principal Component Analysis for interval valued data," Economics & Statistics Discussion Papers esdp03013, University of Molise, Department of Economics.
    • Handle: RePEc:mol:ecsdps:esdp03013
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Roger Millsap & William Meredith, 1988. "Component analysis in cross-sectional and longitudinal data," Psychometrika, Springer;The Psychometric Society, vol. 53(1), pages 123-134, March.
    4. Ledyard Tucker, 1966. "Some mathematical notes on three-mode factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 279-311, September.
    5. 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.
    6. Henk Kiers & Jos Berge, 1989. "Alternating least squares algorithms for simultaneous components analysis with equal component weight matrices in two or more populations," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 467-473, September.
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    Cited by:

    1. Pierpaolo D'Urso & Paolo Giordani, 2006. "A robust fuzzy k-means clustering model for interval valued data," Computational Statistics, Springer, vol. 21(2), pages 251-269, June.
    2. Antonio Irpino & Valentino Tontodonato, 2006. "Clustering reduced interval data using Hausdorff distance," Computational Statistics, Springer, vol. 21(2), pages 271-288, June.

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    More about this item

    Keywords

    Principal Component Analysis; Least squares approach; Interval valued data; Chemical data;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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