El Mostafa Qannari

Defining the underlying sensory dimensions

A hierarchy of three models for analysing sensory profiling data was discussed in a previous paper. The algorithm which determines the parameters of the third model has been improved and a the new version of the algorithm is presented. It is illustrated using the potatoes data proposed by the organisers of the workshop.

Chemometric methods for the coupling of spectroscopic techniques and for the extraction of the relevant information contained in the spectral data tables

The coupling of infrared (IR) and fluorescence spectroscopies was used for studying the modifications affecting proteins during cheese ripening. The data treatment was performed using appropriate chemometric methods: Common Components and Specific Weights Analysis and Canonical Correlation Analysis. These methods demonstrated their ability to describe the overall spectral information collected and to extract the relevant information addressing the modifications of proteins. The results obtained showed that the overall methodology, i.e. coupling of spectroscopies with appropriate chemometric methods, was efficient to monitor modifications of proteins intervening during ripening.

Discrimination on latent components with respect to patterns. Application to multicollinear data

A new presentation of discriminant analysis is discussed. It consists in setting up patterns associated to the various groups and deriving latent variables in such a way that scores in each group are as highly clustered about their pattern as possible. When the conformity between observations and group patterns is investigated by means of the coefficient of correlation, Fishers canonical discriminant analysis is retrieved. If the covariance is used instead of the coefficient of correlation, then a new and simple formalization of PLS discriminant analysis is achieved. The potential of the general approach is discussed and the methods of analysis are illustrated on the basis of a real data set.

Principal component regression, ridge regression and ridge principal component regression in spectroscopy calibration

Ridge regression (RR) and principal component regression (PCR) are two popular methods intended to overcome the problem of multicollinearity which arises with spectral data. The present study compares the performances of RR and PCR in addition to ordinary least squares (OLS) and partial least squares (PLS) on the basis of two data sets. An alternative procedure that combines both PCR and RR is also introduced and is shown to perform well. Furthermore, the performance of the combination of RR and PCR is stable in so far as sufficient information is taken into account. This result suggests discarding those components that are unquestionably identified as noise, when the ridge constant tackles the degeneracy caused by components with small variances.

Segmentation of a panel of consumers using clustering of variables around latent directions of preference

A procedure of clustering of variables is discussed and applied for the purpose of segmenting a panel of consumers. The underlying principle of the method is to find K groups of variables (i.e. the consumers) and K latent components such that the consumers in each group are as much correlated as possible with the corresponding latent component. The procedure involves running, in a first step, a hierarchical clustering algorithm to determine the appropriate number of clusters and an initial partition of consumers. In a second step, a partitioning algorithm is carried out in order to improve the solution thus obtained. This clustering approach is illustrated using two real data sets. On these data sets, the procedure MD-PREF is also performed and it is shown how it can be complemented by the outcomes of the cluster analysis. In particular, indication about the number of clusters among consumers is given.

Segmentation of consumers taking account of external data. A clustering of variables approach

A procedure for clustering of variables is proposed for segmenting a panel of consumers when it is desirable to relate preference of consumers to external data such as sensory data. The underlying principle of the method is to find K groups of variables, associated with the scores of consumers, and K latent components such that the variables in each group are as highly correlated as possible to the corresponding latent component. In addition, the latent components are constrained to be linear combinations of the external data. This approach is complementary to External Preference Mapping. However, it allows a direct segmentation of the panel and involves a smaller number of models than External Preference Mapping.

Comparing generalized procrustes analysis and statis

We consider a model for sensory profiling data including translation, rotation and scaling. We compare two methods to calculate an overall consensus from several data matrices: GPA and STATIS. These methods are briefly illustrated and explained under our model. A series of simulations to compare their performance has been carried out. We found significant differences in performance depending on the variance of random errors and on the dimensionality of the true underlying consensus. Therefore we investigated on the dimensionality of the calculated group averages. We found both methods to give too many dimensions compared to the true consensus. This finding is supported by some theoretical considerations. Finally we propose a combined approach which takes advantage of both methods and which gave better results in the simulations.

A hierarchy of models for analysing sensory data

Abstract We propose a hierarchy of models for averaging sensory profile data. The models follow from formulating the data from each assessor in terms of association matrices and considering different strategies for weighted averaging of these matrices. It turns out that two forms of weighting contained within the hierarchy are very close to Generalised Procrustes Analysis (GPA) and Individual Differences Scaling (INDSCAL). The advantage of the current approach is that the methods are not iterative. The methods are illustrated using data based on perception of yoghurts.

Clustering of variables, application in consumer and sensory studies

We consider two dissimilarity measures between variables that take account of the variances of the variables as well as of their correlations. When variables are standardised, we retrieve widely used dissimilarity measures. The first dissimilarity measure is Euclidean distance and is suitable in studies where negative correlation between variables implies disagreement. The second dissimilarity measure is a Procrustean distance and is suitable in situations where both positive and negative correlations imply agreement. We also discuss aggregation strategies in order to carry out hierarchical clustering and find groups of variables. Applications in consumer and sensory studies are outlined.

Shedding new light on Hierarchical Principal Component Analysis

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