IDEAS home Printed from https://ideas.repec.org/p/mol/ecsdps/esdp03013.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://web.unimol.it/progetti/repec/mol/ecsdps/ESDP03013.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Ledyard Tucker, 1966. "Some mathematical notes on three-mode factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 279-311, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rizzi, Alfredo & Vichi, Maurizio, 1995. "Representation, synthesis, variability and data preprocessing of a three-way data set," Computational Statistics & Data Analysis, Elsevier, vol. 19(2), pages 203-222, February.
    2. Giordani, Paolo, 2010. "Three-way analysis of imprecise data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 568-582, March.
    3. Michel Velden & Tammo Bijmolt, 2006. "Generalized canonical correlation analysis of matrices with missing rows: a simulation study," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 323-331, June.
    4. Tom Wilderjans & E. Ceulemans & I. Mechelen, 2012. "The SIMCLAS Model: Simultaneous Analysis of Coupled Binary Data Matrices with Noise Heterogeneity Between and Within Data Blocks," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 724-740, October.
    5. Ji Yeh Choi & Heungsun Hwang & Marieke E. Timmerman, 2018. "Functional Parallel Factor Analysis for Functions of One- and Two-dimensional Arguments," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 1-20, March.
    6. Kohei Adachi, 2013. "Generalized joint Procrustes analysis," Computational Statistics, Springer, vol. 28(6), pages 2449-2464, December.
    7. Takane, Yoshio & Hwang, Heungsun, 2005. "An extended redundancy analysis and its applications to two practical examples," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 785-808, June.
    8. Mariela González-Narváez & María José Fernández-Gómez & Susana Mendes & José-Luis Molina & Omar Ruiz-Barzola & Purificación Galindo-Villardón, 2021. "Study of Temporal Variations in Species–Environment Association through an Innovative Multivariate Method: MixSTATICO," Sustainability, MDPI, vol. 13(11), pages 1-25, May.
    9. Yuefeng Han & Rong Chen & Dan Yang & Cun-Hui Zhang, 2020. "Tensor Factor Model Estimation by Iterative Projection," Papers 2006.02611, arXiv.org, revised May 2022.
    10. Elisa Frutos-Bernal & Ángel Martín del Rey & Irene Mariñas-Collado & María Teresa Santos-Martín, 2022. "An Analysis of Travel Patterns in Barcelona Metro Using Tucker3 Decomposition," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    11. Xinhai Liu & Wolfgang Glänzel & Bart De Moor, 2011. "Hybrid clustering of multi-view data via Tucker-2 model and its application," Scientometrics, Springer;Akadémiai Kiadó, vol. 88(3), pages 819-839, September.
    12. Yoshio Takane & Forrest Young & Jan Leeuw, 1977. "Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 42(1), pages 7-67, March.
    13. Dawn Iacobucci & Doug Grisaffe, 2018. "Perceptual maps via enhanced correspondence analysis: representing confidence regions to clarify brand positions," Journal of Marketing Analytics, Palgrave Macmillan, vol. 6(3), pages 72-83, September.
    14. Giuseppe Brandi & Ruggero Gramatica & Tiziana Di Matteo, 2019. "Unveil stock correlation via a new tensor-based decomposition method," Papers 1911.06126, arXiv.org, revised Apr 2020.
    15. Pierpaolo D’Urso & Marta Disegna & Riccardo Massari, 2020. "Satisfaction and Tourism Expenditure Behaviour," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(3), pages 1081-1106, June.
    16. Eric Jondeau & Emmanuel Jurczenko & Michael Rockinger, 2018. "Moment Component Analysis: An Illustration With International Stock Markets," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(4), pages 576-598, October.
    17. 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.
    18. Ventura L. Charlin & Steve Sussman & Clyde W. Dent & Alan W. Stacy & John W. Graham & Marny Barovich & Ginger Hahn & Dee Burton & Brian R. Flay, 1990. "Three Methods of Assessing Adolescent School-Level Experimentation of Tobacco Products," Evaluation Review, , vol. 14(3), pages 297-307, June.
    19. Kiers, Henk A. L., 1998. "Three-way SIMPLIMAX for oblique rotation of the three-mode factor analysis core to simple structure," Computational Statistics & Data Analysis, Elsevier, vol. 28(3), pages 307-324, September.
    20. Krijnen, Wim P., 2006. "Convergence of the sequence of parameters generated by alternating least squares algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 481-489, November.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mol:ecsdps:esdp03013. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Claudio Lupi (email available below). General contact details of provider: https://edirc.repec.org/data/dsmolit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.