Principal Component Analysis (PCA) is a well-known tool often used for the exploratory analysis of a numerical data set. Here an extension of classical PCA is proposed, which deals with fuzzy data (in short PCAF), where the elementary datum cannot be recognized exactly by a specific number but by a center, two spread measures and a membership function. Specifically, two different PCAF methods, associated with different hypotheses of interrelation between parts of the solution, are proposed. In the first method, called Centers-related Spread PCAF (CS-PCAF), the size of the spread measures depends on the size of the centers. In the second method, called Loadings-related Spread PCAF (LS-PCAF), the spreads are not related directly to the sizes of the centers, but indirectly, via the component loadings. To analyze how well PCAF works a simulation study was carried out. On the whole, the PCAF method performed better than or equally well as PCA, except in a few particular conditions. Finally, the application of PCAF to an empirical fuzzy data set is described. (C) 2002 Elsevier B.V. All rights reserved.

Principal Component Analysis of symmetric fuzzy data / Giordani, Paolo; Henk A. L., Kiers. - In: COMPUTATIONAL STATISTICS & DATA ANALYSIS. - ISSN 0167-9473. - 45:3(2004), pp. 519-548. [10.1016/s0167-9473(02)00352-3]

Principal Component Analysis of symmetric fuzzy data

GIORDANI, Paolo;
2004

Abstract

Principal Component Analysis (PCA) is a well-known tool often used for the exploratory analysis of a numerical data set. Here an extension of classical PCA is proposed, which deals with fuzzy data (in short PCAF), where the elementary datum cannot be recognized exactly by a specific number but by a center, two spread measures and a membership function. Specifically, two different PCAF methods, associated with different hypotheses of interrelation between parts of the solution, are proposed. In the first method, called Centers-related Spread PCAF (CS-PCAF), the size of the spread measures depends on the size of the centers. In the second method, called Loadings-related Spread PCAF (LS-PCAF), the spreads are not related directly to the sizes of the centers, but indirectly, via the component loadings. To analyze how well PCAF works a simulation study was carried out. On the whole, the PCAF method performed better than or equally well as PCA, except in a few particular conditions. Finally, the application of PCAF to an empirical fuzzy data set is described. (C) 2002 Elsevier B.V. All rights reserved.
2004
fuzzy data sets; least squares approach; principal component analysis
01 Pubblicazione su rivista::01a Articolo in rivista
Principal Component Analysis of symmetric fuzzy data / Giordani, Paolo; Henk A. L., Kiers. - In: COMPUTATIONAL STATISTICS & DATA ANALYSIS. - ISSN 0167-9473. - 45:3(2004), pp. 519-548. [10.1016/s0167-9473(02)00352-3]
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/146544
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 39
  • ???jsp.display-item.citation.isi??? 32
social impact