Michel Tenenhaus

• PhD
• Professor Emeritus at HEC Paris

A new framework for sequential multiblock component methods is presented. This framework relies on a new version of regularized generalized canonical correlation analysis (RGCCA) where various scheme functions and shrinkage constants are considered. Two types of between block connections are considered: blocks are either fully connected or connecte...

A new framework for many multiblock component methods (including consensus and hierarchical PCA) is proposed. It is based on the consensus PCA model: a scheme connecting each block of variables to a superblock obtained by concatenation of all blocks. Regularized consensus PCA is obtained by applying regularized generalized canonical correlation ana...

a b s t r a c t This paper presents an overview of methods for the analysis of data structured in blocks of variables or in groups of individuals. More specifically, regularized generalized canonical correlation analysis (RGCCA), which is a unifying approach for multiblock data analysis, is extended to be also a unifying tool for mul-tigroup data a...

This paper presents an overview of methods for the analysis of data structured in blocks of variables or in groups of individuals. More specifically, regularized generalized canonical correlation analysis (RGCCA), which is a unifying approach for multiblock data analysis, is extended to be also a unifying tool for mul-tigroup data analysis. The ver...

This paper presents an overview of methods for the analysis of data structured in blocks of variables or in groups of individuals. More specifically, regularized generalized canonical correlation analysis (RGCCA), which is a unifying approach for multiblock data analysis, is extended to be also a unifying tool for mul-tigroup data analysis. The ver...

The majority of the studies conducted on sleep deprivation has been dedicated to the consequences on the psychomotor performances. However, the impact of a debt of sleep on the skin has never been studied to date. Fourteen Caucasian females subjects (30-40 years) were included in this study that consisted in 3 sessions: baseline session (2 days), c...

L'analyse canonique généralisée régularisée (RGCCA pour Regularized Generalized Canonical Correlation Analysis) a été récemment proposée par Tenenhaus et Tenenhaus (2011) pour l'analyse des tableaux multiples. RGCCA unifie des méthodes d'analyse de tableaux multiples basées sur la maximisation d'un critère de corrélation et/ou de covariance entre l...

Regularized generalized canonical correlation analysis (RGCCA) is a generalization of regularized canonical correlation analysis to three or more sets of variables. It constitutes a general framework for many multi-block data analysis methods. It combines the power of multi-block data analysis methods (maximization of well identified criteria) and...

The objective of this paper is to describe the use of unweighted least squares (ULS) structural equation modeling (SEM) and partial least squares (PLS) path modeling in a regression model relating two blocks of binary variables, when a group effect can influence the relationship. Two sets of binary variables are available. The first set is defined...

In data analysis of social, economic and technical fields, compositional data is widely used in problems of proportions to the whole. This paper develops regression modelling methods of compositional data, discussing the relationships of one compositional data to one or more than one compositional data and the interrelationship of multiple composit...

A situation where J blocks of variables X 1, …, X J are observed on the same set of individuals is considered in this paper. A factor analysis approach is applied to blocks instead of variables. The latent variables (LV’s) of each block should well explain their own block and at the same time the latent variables of same order should be as highly...

Nous donnons dans cette communication une définition de l'analyse canonique généralisée au niveau de la population (ACG-population) qui constitue le cadre théorique de l'approche PLS proposée par Herman Wold et à ses extensions proposées par Jan-Bernd Lohmöller et Nicole Krämer. En écrivant les équations stationnaires de l'ACG-population au niveau...

Regularized generalized canonical correlation analysis (RGCCA) is a generalization of regularized canon-ical correlation analysis to 3 or more sets of variables. RGCCA is a component-based approach which aims to study the relationships between several sets of variables. The quality and interpretability of the RGCCA components are likely to be affec...

Structural equation models (SEMs) make it possible to estimate the causal relationships, defined according to a theoretical model, linking two or more latent complex concepts, each measured through a number of observable indicators, usually called manifest variables. Traditionally, the component-based estimation of SEMs by means of partial least sq...

Two complementary schools have come to the fore in the field of Structural Equation Modelling (SEM): covariance-based SEM and component-based SEM. The first approach has been developed around Karl Joreskog and the second one around Herman Wold under the name 'PLS' (Partial Least Squares). Hwang and Takane have proposed a new component-based SEM met...

Résumé Deux écoles concurrentes se sont imposées dans le domaine de la modélisation des équations structurelles. La première approche, appelée « Covariance-based SEM » (SEM = Structural Equation Modeling), s'est développée autour de Karl Jöreskog. Cette approche a pour objectif de modéliser la matrice de covariance des variables observées. Elle peu...

Current classifications of healthy skin are based on a limited number of characteristics such as oiliness or susceptibility to sun exposure. The aim of this study, carried out on 259 Caucasian women aged between 20 and 50, was to establish a classification of healthy facial skin irrespective of age, based on visual and tactile characteristics, usin...

Two complementary schools have come to the fore in the field of Structural Equation Modelling (SEM): covariance-based SEM and component-based SEM. The first approach developed around Karl Jöreskog. It can be considered as a generalisation of both principal component analysis and factor analysis to the case of several data tables connected by causal...

This research aims at assessing the influence of baseline skin colour on the ability of reflectance spectrophotometry to detect cutaneous erythema induced by a low concentration of methyl nicotinate (2.5 mM) (first objective), and to detect tanning induced by ultraviolet rays (UVA+UVB) at infra-erythemal doses (second objective). Two independent st...

Skin properties, such as colour, hydration and texture, can be studied on a qualitative basis by a clinical assessment or on a quantitative basis using techniques that measure biophysical properties of the skin. The aim of this study was to explore the links between facial skin features and a range of skin biophysical parameters using multivariate...

A reliable panel is required in sensory analysis. The purpose of this paper is to propose a new methodology based on a mixed linear model to test various criteria of a panel’s reliability. The developed method allows testing the global performance of the panel, and the individual performances of each judge in terms of discriminability and repeatabi...

Phototype classifications were initially developed in an attempt to predict the skin reactions of patients to phototherapy and are now widely used to advise individuals with regard to sun protection. A transversal study was conducted on the SU.VI.MAX cohort to estimate the frequency of sun-reactive skin features in a large, general adult population...

This paper depicts a methodology devoted to a situation where a few products are described by many physico-chemical and sensory characteristics, and are evaluated by consumers on a preference scale. The objective is to relate the block of hedonic variables to the physico-chemical and to the sensory blocks. The analysis of the link between the respo...

With advances in high-density cDNA micro-array technology, molecular predictors can become a very useful diagnostic tool to predict survival probability on the basis of gene expression. In the context of censored data, the Cox model, like multivariate regression models, supposes that there are more observations than variables, complete data, and va...

A situation where J blocks of variables are observed on the same set of individuals is considered in this paper. A factor analysis logic is applied to tables instead of variables. The latent variables of each block should well explain their own block and, at the same time, the latent variables of same order should be as positively correlated as pos...

A presentation of the Partial Least Squares approach to Structural Equation Modeling (or PLS Path Modeling) is given together with a discussion of its extensions. This approach is compared with the estimation of Structural Equation Modeling by means of maximum likelihood (SEMML). Notwithstanding, this approach still shows some weaknesses. In this r...

PLS univariate regression is a model linking a dependent variable y to a set X={x1, …, xp} of (numerical or categorical) explanatory variables. It can be obtained as a series of simple and multiple regressions. By taking advantage from the statistical tests associated with linear regression, it is feasible to select the significant explanatory vari...

A situation where J blocks of variables are observed on the same set of individuals is considered in this paper. A factor analysis logic is applied to tables instead of individuals. The latent variables of each block should explain their own block well and at the same time the latent variables of the same rank should be as positively correlated as...

Abstract PLS univariate regression is a model linking a dependent variable y to a set X = {x1 ;:::; xp} of (numerical or categorical) explanatory variables. It can be obtained as a series of simple and multiple regressions. By taking advantage from the statistical tests associated with linear regression, it is feasible to select the signi6cant expl...

A situation where J blocks of variables are observed on the same set of individuals is considered. A factor analysis logic is applied to tables instead of individuals. The latent variables of each block should well explain their own block and in the same time the latent variables of the same rank should be as positively correlated as possible. In t...

PLS regression and multiple imputation

A method for mapping complex trait genes using cDNA microarray and molecular marker data jointly is presented and illustrated via simulation. We introduce a novel approach for simulating phenotypes and genotypes conditionally on real, publicly available, microarray data. The model assumes an underlying continuous latent variable (liability) related...

Partial least squares discriminant analysis (PLS-DA) is a partial least squares regression of a set Y of binary variables describing the categories of a categorical variable on a set X of predictor variables. It is a compromise between the usual discriminant analysis and a discriminant analysis on the significant principal components of the predict...

There are various ways to deal with missing data. Among the conventional methods for handling missing data "listewise deletion" could be considered as a safer or less biaised approach. However if the amount of data that must be discarded under listwise deletion is dramatic other alternatives must be considered. A first strategy is the simple imputa...

To assess the relative contribution of intrinsic aging vs lifestyle factors to facial skin age. Prospective analysis of a cohort. Skin research institute. A cohort of 361 white women (age range, 18-80 years) with apparently healthy skin. Visual and tactile assessment of facial skin features. Twenty-four skin characteristics were used to build a ski...

PLS generalized regression : Application to the analysis of life time data

PLS generalized regression: Application to the analysis of life time data

The purpose of this paper is to present PLS Path Modeling, to describe the various options of LVPLS 1.8 and PLS-Graph 3.0 for carrying out a path model, and to comment the output of both software. PLS-Graph 3.0 is actually based on LVPLS 1.8. As an added value, PLS-Graph has a very friendly graphical interface for drawing the model and a resampling...

" Stepwise PLS regression and multiple regression, Application to the selection of variables, the choice of the number of PLS components and PLS generalized linear regression " CIRO'02. Marrakech, Juin 2002.

Cahier de Recherche du Groupe HEC, n° 766/2002 ISBN : 2-85418-766-0

Many statistical methods can be used to study data presented in the form of J blocks of variables observed on the same subjects. The most well-known methods are the following: Horst's generalised canonical correlation analysis, Carroll's generalised canonical correlation analysis, Escofier and Pagès' multiple factor analysis and second order confir...

Multiple Factor Analysis (MFA) highlights the structures common to a set of J groups (or blocks) of variables observed for the same individuals. PLS path modelling allows a search for latent variables, summarising as far as possible one-dimensional blocks of manifest variables while taking account of causal links between the blocks. These two metho...

PLS generalized linear regression. Application to the analysis of life time data

PLS generalized linear regression : Application to the analysis of life time data

SUMMARY Problems encountered in multiple regression due to multicolinearity or missing data can be overcome by using PLS regression. Several versions of the PLS regression algorithm exist. In this paper, we present a new version of this algorithm which can be extended to generalized linear regression models such as ordinal or multinomial logistic r...

Background.- Although skin disorders associated with long-term sun exposure account for high morbidity, only few data on sun-related preclinical skin changes are available in the general population.objective: In the present study we determined reference values for markers of photoaging in French adults, and we evaluated the relationship between pho...

The European Consumer Satisfaction Index (ECSI) is an economic indicator that measures customer satisfaction. It is an adaptation of the Swedish Customer Satisfaction Barometer and is compatible with the American Customer Satisfaction Index. In this paper the ECSI model is presented in details. The PLS approach used to estimate the model parameters...

Cahier de Recherche du Groupe HEC Paris, n° 643

Cahier de Recherche du Groupe HEC Paris, n° 550

Cahier de Recherche du Groupe HEC Paris, n° 540

Régression PLS et applications.

Cahier de Recherche du Groupe HEC Paris, n° 472

Cahier de Recherche du Groupe HEC Paris, n° 435

Canonical analysis of two convex polyhedral cones consists in looking for two vectors (one in each cone) whose square cosine is a maximum. This paper presents new results about the properties of the optimal solution to this problem, and also discusses in detail the convergence of an alternating least squares algorithm. The set of scalings of an ord...

Cahier de Recherche du Groupe HEC Paris, n° 306

Cahier de Recherche du Groupe HEC Paris, n° 283

We discuss a variety of methods for quantifying categorical multivariate data. These methods have been proposed in many different countries, by many different authors, under many different names. In the first major section of the paper we analyze the many different methods and show that they all lead to the same equations for analyzing the same dat...

Cahier de Recherche du Groupe HEC, N° 87

The elements of a population evolving during the course of time are described by means of various characteristics. It is attempted to represent this multidimensional time series in a reduced dimension space in order to visualize the evolution of the phenomenon while at the same time minimizing the reduction of the dimensions. On the other hand the...

Conférence réalisée le 1 er décembre 2004 par Christiane Guinot {christiane.guinot@ceries-lab.com} dans le cadre du cycle « Jean-Pierre Fénelon ». Les résultats de cette recherche ont été publiés dans les actes de trois différents congrès scientifiques Européens [5,15-16]. Résumé Une exposition solaire excessive engendre une accélération du vieilli...

The objective of this paper is to describe the use of unweighted least squares (ULS) structural equation modeling (SEM) and partial least squares (PLS) path modeling in a regression model relating two blocks of binary variables when a group effect can influence the relationship. Two sets of binary variables are available. The first set is defined b...