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Dive into the research topics where Mohamed Hanafi is active.

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Featured researches published by Mohamed Hanafi.


Computational Statistics & Data Analysis | 2006

Analysis of K sets of data, with differential emphasis on agreement between and within sets

Mohamed Hanafi; Henk A. L. Kiers

A general class of methods for (partial) rotation of a set of (loading) matrices to maximal agreement has been available in the literature since the 1980s. It contains a generalization of canonical correlation analysis as a special case. However, various other generalizations of canonical correlation analysis have been proposed. A new general class of methods for each such alternative generalization of canonical correlation is proposed. Together, these general classes of methods form a superclass of methods that strike a compromise between explaining the variance within sets of variables and explaining the agreement between sets of variables, as illustrated in some examples. Furthermore, one general algorithm for finding the solutions for all methods in all general classes is offered. As a consequence, for all methods in the superclass of methods, algorithms are available at once. For the existing methods, the general algorithm usually reduces to the standard algorithms employed in these methods, and thus the algorithms for all these methods are shown to be related to each other.


Archive | 2010

A Bridge Between PLS Path Modeling and Multi-Block Data Analysis

Michel Tenenhaus; Mohamed Hanafi

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 correlated as possible (positively or in absolute value). Two path models can be used in order to obtain the first order latent variables. The first one is related to confirmatory factor analysis: each LV related to one block is connected to all the LV’s related to the other blocks. Then, PLS path modeling is used with mode A and centroid scheme. Use of mode B with centroid and factorial schemes is also discussed. The second model is related to hierarchical factor analysis. A causal model is built by relating the LV’s of each block X j to the LV of the super-block X J + 1 obtained by concatenation of X 1, …, X J . Using PLS estimation of this model with mode A and path-weighting scheme gives an adequate solution for finding the first order latent variables. The use of mode B with centroid and factorial schemes is also discussed. The higher order latent variables are found by using the same algorithms on the deflated blocks. The first approach is compared with the MAXDIFF/MAXBET Van de Geer’s algorithm (1984) and the second one with the ACOM algorithm (Chessel and Hanafi, 1996). Sensory data describing Loire wines are used to illustrate these methods.


Journal of Chemometrics | 2010

Shedding new light on Hierarchical Principal Component Analysis

Mohamed Hanafi; Achim Kohler; El Mostafa Qannari

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


GfKl | 2006

Assessing Unidimensionality within PLS Path Modeling Framework

Mohamed Hanafi; Mostafa El Qannari

In very many applications and, in particular, in PLS path modeling, it is of paramount importance to assess whether a set of variables is unidimensional. For this purpose, different methods are discussed. In addition to methods generally used in PLS path modeling, methods for the determination of the number of components in principal components analysis are considered. Two original methods based on permutation procedures are also proposed. The methods are compared to each others by means of a simulation study.


Computational Statistics & Data Analysis | 2008

Continuum redundancy-PLS regression: A simple continuum approach

S. Bougeard; Mohamed Hanafi; El Mostafa Qannari

The relationships between two data sets are investigated. The aim is to predict one data set from the other. New formulations of Redundancy Analysis and Partial Least Square Regression (PLS) are discussed, clearly showing the connexions between these two popular methods. Moreover, it is shown that the Redundancy Analysis and PLS regression are the two end points of a continuum approach. Properties related to this continuum approach are discussed, showing how the multicolinearity problem is handled. The interest of the general strategy of analysis is illustrated on the basis of a data set pertaining to epidemiology.


Computational Statistics & Data Analysis | 2005

An alternative algorithm to the PLS B problem

Mohamed Hanafi; El Mostafa Qannari

The PLS B algorithm is used as a tool to investigate the relationships among several data sets. The first step of this algorithm entails an iterative procedure the convergence of which is not proved. In this paper, an alternative procedure is discussed. It achieves the same purpose and its convergence is proven.


Computational Statistics & Data Analysis | 2015

Multi-way PLS regression

Mohamed Hanafi; Samia Ouertani; Julien Boccard; Serge Rudaz

The tri-linear PLS2 iterative procedure, an algorithm pertaining to the NIPALS framework, is considered. It was previously proposed as a first stage to estimate parameters of the multi-way PLS regression method. It is shown that the tri-linear PLS2 procedure is convergent. The procedure generates a sequence of parameters (scores and loadings), which can be described as increasing or decreasing two specific criteria. Furthermore, a hidden tensor is described allowing tri-linear PLS2 to search its best rank-one approximation. This tensor highlights the link between multi-way PLS regression and the well-known PARAFAC model. The parameters of the multi-way PLS regression method can be computed using three alternative procedures. It is shown that the tri-linear PLS2 procedure is convergent.The sequences generated by the tri-linear PLS2 can be described as increasing or decreasing two specific criteria.A hidden tensor is described allowing tri-linear PLS2 to search its best rank one approximation.A link between multi-way PLS regression and the well-known PARAFAC model is highlighted.


Journal of Chemometrics | 2012

Quadratic PLS1 regression revisited

Stéphane Verdun; Mohamed Hanafi; Véronique Cariou; El Mostafa Qannari

Within the framework of nonlinear partial least squares (PLS), the quadratic PLS regression approach, involving both linear and quadratic terms in the criterion, is discussed. A new algorithm for the determination of the components is proposed, and its advantages over the original algorithm are outlined. The approach of analysis is illustrated on the basis of simulated and real data. Copyright


7th Meeting of the Partial Least Squares (PLS). Univ Texas, Houston, TX, MAY 19-22, 2012 | 2013

Multiblock and Path Modeling with OnPLS

Tommy Löfstedt; Mohamed Hanafi; Johan Trygg

OnPLS was recently proposed as a general extension of O2PLS for applications in multiblock and path model analysis. OnPLS is very similar to O2PLS in the case with two matrices, but generalizes symmetrically to cases with more than two matrices without giving preference to any matrix.


Chemometrics and Intelligent Laboratory Systems | 2006

Common components and specific weights analysis: A chemometric method for dealing with complexity of food products

Mohamed Hanafi; E. Dufour; Dominique Bertrand; El Mostafa Qannari

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El Mostafa Qannari

Institut national de la recherche agronomique

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Achim Kohler

Norwegian University of Life Sciences

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Serge Rudaz

University of Lausanne

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Dominique Bertrand

Institut national de la recherche agronomique

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Sahar Hassani

Norwegian University of Life Sciences

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Stéphanie Ledauphin

Institut national de la recherche agronomique

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