Vertices Principal Component Analysis (V-PCA) and Centers Principal Component Analysis (C-PCA) are variants of Principal Component Analysis (PCA) to deal with two-way interval-valued data. In this case the observation units are represented as hyperrectangles instead of points. Tucker3 and CANDECOMP/PARAFAC are component analysis techniques to analyze the underlying structure of three-way data sets. In the present paper, after recalling the above mentioned methods, we extend the C-PCA and V-PCA methods to deal with three-way interval-valued data by means of Tucker3 and CANDECOMP/PARAFAC and we describe how to represent the observation units in the obtained low-dimensional space. Furthermore, an application of the extended methods—called Three-way Vertices Principal Component Analysis (3V-PCA) and Three-way Centers Principal Component Analysis (3C-PCA) to three-way interval-valued air pollution data is described.

Three-way component analysis of interval valued data / Giordani, Paolo; Kiers, H. A. L.. - In: JOURNAL OF CHEMOMETRICS. - ISSN 0886-9383. - STAMPA. - 18:(2004), pp. 253-264. [10.1002/cem.868]

Three-way component analysis of interval valued data

GIORDANI, Paolo;
2004

Abstract

Vertices Principal Component Analysis (V-PCA) and Centers Principal Component Analysis (C-PCA) are variants of Principal Component Analysis (PCA) to deal with two-way interval-valued data. In this case the observation units are represented as hyperrectangles instead of points. Tucker3 and CANDECOMP/PARAFAC are component analysis techniques to analyze the underlying structure of three-way data sets. In the present paper, after recalling the above mentioned methods, we extend the C-PCA and V-PCA methods to deal with three-way interval-valued data by means of Tucker3 and CANDECOMP/PARAFAC and we describe how to represent the observation units in the obtained low-dimensional space. Furthermore, an application of the extended methods—called Three-way Vertices Principal Component Analysis (3V-PCA) and Three-way Centers Principal Component Analysis (3C-PCA) to three-way interval-valued air pollution data is described.
2004
01 Pubblicazione su rivista::01a Articolo in rivista
Three-way component analysis of interval valued data / Giordani, Paolo; Kiers, H. A. L.. - In: JOURNAL OF CHEMOMETRICS. - ISSN 0886-9383. - STAMPA. - 18:(2004), pp. 253-264. [10.1002/cem.868]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/146543
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