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Analyzing multiset data by the Power STATIS-ACT method

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Abstract

The STATIS-ACT method is a generalization of principal component analysis used to study simultaneously several data tables measured on the same observation units or variables. The goal of this method is to analyze the relationship between these data tables and to combine them into a compromise matrix corresponding to an optimal agreement between the data. In this paper, we propose a new approach to this method, referred to as the Power STATIS-ACT method, where the compromise matrix is derived from a general s-power based criterion \({(s\geqslant 1)}\) and investigate some of its theoretical and practical properties. Special attention is devoted to the 1-power case which makes the introduction of low rank versions of the compromise possible. We also examine the effect of varying the power parameter s on the compromise solutions. All results are illustrated with a number of real data tables.

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Authors and Affiliations

  1. IRMAR, UMR CNRS 6625, Université Rennes 2, Place du Recteur Henri Le Moal, CS 24307, 35043, Rennes Cedex, France

    Jacques Bénasséni & Mohammed Bennani Dosse

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  1. Jacques Bénasséni
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  2. Mohammed Bennani Dosse
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Correspondence to Mohammed Bennani Dosse.

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The authors are obliged to the editors and referees for helpful suggestions.

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Bénasséni, J., Bennani Dosse, M. Analyzing multiset data by the Power STATIS-ACT method. Adv Data Anal Classif 6, 49–65 (2012). https://doi.org/10.1007/s11634-011-0085-8

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  • DOI: https://doi.org/10.1007/s11634-011-0085-8

Keywords

Mathematics Subject Classification (2000)