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Shedding new light on Hierarchical Principal Component Analysis

Authors

  • Mohamed Hanafi,

    Corresponding author
    1. ONIRIS, Unité de Sensométrie et de Chimiométrie, site de la Géraudière, BP 82225, 44322 Nantes Cedex 3, France
    2. Université Nantes Angers Le Mans, France
    • ONIRIS, Unité de Sensométrie et de Chimiométrie, site de la Géraudière, BP 82225, 44322 Nantes Cedex 3, France.
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  • Achim Kohler,

    1. NOFIMA MAT, Center for Biospectroscopy and Data Modelling, Osloveien 1, 1430 ÅS, Norway
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  • El Mostafa Qannari

    1. ONIRIS, Unité de Sensométrie et de Chimiométrie, site de la Géraudière, BP 82225, 44322 Nantes Cedex 3, France
    2. Université Nantes Angers Le Mans, France
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Abstract

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 © 2010 John Wiley & Sons, Ltd.

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