Three‐way component analysis of interval‐valued data

Abstract

AbstractVertices 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. Copyright © 2004 John Wiley & Sons, Ltd.