Une n-acp d'un hypercube de donnees
Esteban Polit Montes de · 1986
The model proposed by tucker for analysing 3 modes data sets is extended to the n-modes setting and metrics are introduced for analysing each mode. One assotiates an n-linear form to each n-mode data set and approches by an n-linear form of smaller rank, that defines a n-mode data set of reduced sizes, easier to analyse. We propose an algorithm named tuckalsn that solves the approximation problem involved in extending the iterative process given by kroonenberg and de leeuw. The latent variables, so obtained, are shown to extenoed principal components built by usual 2 modes pca, and received analogous interpretations. We discuss too the optimality properties of usual pca that remain true or not in the n-modes setting. Graphical representations as well as interpretative tools for reading them are proposed, such as indices meaning the global and elementwise quality and reliability of the approximation.