A SINGULAR-VALUE DECOMPOSITION OF AN ELEM ENT BELONGING TO A TENSOR PRODUCT OF KAPPA SEPARABLE HILBERT-SPACES

Using a tensorial approach, Leibovici (see [6]) has already explained a very simple theoretic and practical way to obtain the Singular Value Decomposition of multi-way arrays. Based on this presentation, we der ive the same analysis in separable Hilbert spaces. This permits us to find again the PCA of several curves and PCA of a process, but we can also derive a PCA of a multivariate process via the PTA-3modes method, and so on via the PTA-kmodes method. Proofs of convergence properties of PCA are redescribed within this approach and extended for the PTA- kmodes method.