Research activities
Brigitte Le Roux’s research activities are organised around Geometric Data Analysis (GDA), that is, methods of multidimensional Euclidean analysis and their applications to the human and biological sciences.
Geometric Data Analysis (GDA) — Foundations
My work on the stability of Euclidean clouds began within the mathematical statistics laboratory of the ISUP (directed by J.-P. Benzécri). From 1971 to 1979, with Brigitte Escofier, I studied stability problems within the framework of Principal Component Analysis (PCA) and Correspondence Analysis (CA), in particular the rotation of invariant subspaces of a symmetric endomorphism under rank-one perturbations (cf. key articles [1972], [1977]).
The central objective is to study the sensitivity of the methods for determining principal axes and variables in CA, MCA and PCA under different types of modification: changes to the Euclidean structure, point removal or addition, grouping. This work is widely referenced in the international literature on multivariate analysis (Lebart, Greenacre, Gifi) and has been extended in the sensitivity analysis framework (Benasseni, Pack & Joliffe, Lauro & Balbi). A synthesis appears in Chapter 7 of Geometric Data Analysis (Kluwer, 2004).
Multiple Correspondence Analysis (MCA)
MCA is at the heart of the programme for the international dissemination of GDA. The monograph Multiple Correspondence Analysis (Sage QASS Series no. 163, 2010), co-authored with Henry Rouanet, presents the principles of the method, its application to the “taste” example, structured data analysis and inductive data analysis, with two full-scale research studies: the French field of publishers and the Norwegian field of power.
Structured Data Analysis
Within the Group Mathematics and Psychology (CNRS / Université René Descartes), research focused on a synthesis between data analysis and the analysis of variance (Rouanet & Lépine), giving rise to structured data analysis: the analysis of clouds endowed with classical experimental designs (crossing, nesting). This theme is one of the research axes of the MAP5 team (CNRS / Université Paris 5) and is developed in Chapter 6 of the Kluwer book (2004) and Chapter 4 of the MCA monograph (2010).
Combinatorial Inference in GDA
My research on inference in data analysis first addressed the extension of the test value notion for comparing groups in PCA and MCA (Chapter 4 of the HDR; [1998]). This line of work culminated in the book Combinatorial Inference in Geometric Data Analysis (Chapman & Hall/CRC, 2019), co-authored with Solène Bienaise and Jean-Luc Durand, which develops a combinatorial approach to typicality and homogeneity tests applied to Euclidean clouds.
Applications in the Human and Biological Sciences
Over recent years I have conducted in-depth collaborations in several domains:
- Sociology and political space: with H. Rouanet, J. Chiche and P. Perrineau (CEVIPOF, Sciences Po Paris) — study of French electorates based on the 2002 electoral surveys; Franco-Norwegian project (AURORA/EGIDE programme, 2003–2005) with O. Korsnes (University of Bergen) on a comparative study of social spaces in France and Norway.
- Cognitive psychology: EPGY project — analysis of individual differences among gifted students participating in the Educational Program for Gifted Youth (Stanford University, at the invitation of Patrick Suppes).
- Biological sciences: Snack for diabetic children project (co-supervision of EPHE doctoral thesis with J. Louis-Sylvestre); collaboration on compliance among insulin-dependent young diabetics (Université Paris 7).
These applications in turn feed back into theoretical advances, including specific analysis (cf. [1999]).
International Dissemination
The dissemination of GDA methods has relied on organising workshops in several countries: Uppsala (Sweden, annually since 2006), Copenhagen (Denmark, 2009), Lausanne (Switzerland, 2011), Kaliningrad (Russia, 2012), Berkeley (California, 2012), Mendoza (Argentina, 2013), Potsdam (Germany, 2017).