Three-way component analysis of interval valued data

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.