Shedding new light on Hierarchical Principal Component Analysis
Hierarchical Principal Component Analysis (HPCA) is a multiblock method which is designed to reveal covariant patterns between and within several multivariate datasets. The computation of the parameters of this method, namely block scores, block loadings, global loadings and global scores, is based on an iterative procedure. However, very few properties are known regarding the convergence of this iterative procedure. The paper discloses a monotony property of HPCA and exhibits an optimization criterion for which HPCA algorithm provides a monotonic convergent solution. This makes it possible to shed a new light on this method of analysis by showing new properties and pinpointing its relation to existing methods such as Common Component and Specific weights Analysis (CCSWA), INDSCAL and PARAFAC Models. Copyright (C) 2010 John Wiley & Sons, Ltd.
hierarchical principal component analysis common component and specific weights analysis indscal parafac nipals