Symbolic Factor Analysis

  • Hans-Hermann Bock
  • A. Chouakria
  • P. Cazes
  • E. Diday
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

In the present chapter we propose an extension of the standard principal component analysis method which takes as input a symbolic data matrix \(\underline X = ({\xi _{ij}})\) of interval type (Chouakria 1994, 1995, Cazes 1997; see section 3.2). Each ‘value’ \({\xi _{ij}}\) is an interval containing all the possible values of the feature Y j for an object iE (or i ∈ Ω). Instead of representing each object i and its description x i by a single point on a factorial plane in \({\mathbb{R}^2}\) (or \({\mathbb{R}^s}\)) as in classical principal component analysis (PCA), the proposed method visualizes each object i by a rectangle in \({\mathbb{R}^2}\) . Whereas the classical PCA is briefly sketched in section 9.1, we describe our generalized method in section 9.2. Thereby, we present a typical example concerning oils and fats in order to illustrate the effectiveness of the proposed symbolic PCA method.

Keywords

Covariance Iodine Diesel Petrol Val1 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Hans-Hermann Bock
    • 1
  • A. Chouakria
    • 2
    • 3
  • P. Cazes
    • 2
  • E. Diday
    • 2
  1. 1.Institut für StatistikRWTH AachenGermany
  2. 2.LISE-CEREMADEUniversité Paris IX — DauphineFrance
  3. 3.INRIA-RoquencourtLe ChesnayFrance

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