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Often in analytical practice, a set of samples is described by different types of measurements in the hope that a comprehensive characterisation of samples will provide a more complete picture and will help in determining the similarities among samples. The main focus is then on how to combine the information described by different measurement variables and how to analyse it simultaneously. In other words, the main goal is to find a common representation of samples that emphasises the individual and common properties of the different blocks of variables. Several methods can be adopted for the simultaneous analysis of multiblock data with a common object mode. These are: consensus principal component analysis (CPCA), SUM-PCA, multiple factor analysis (MFA) and structuration des tableaux à trois indices de la statistique (STATIS).In this article we present a comparison of the performances of these methods for data describing the chemistry and sensory profiles of the Maillard reaction products. The aroma compounds formed during the reaction of thermal heating between one or two selected amino acids and one or two reducing sugars have been analysed by head space gas chromatography and the intensity and nature of the odour of the resulting products has been evaluated according to selected descriptors by a panel of sensory experts.The results showed that using the information of the chromatographic and sensory data in conjunction enhanced the interpretability of the data. SUM-PCA and more specifically multiple factor analysis, MFA, allowed for a detailed study of the similarities of mixtures in terms of reaction products and sensory profiles.

Feature selection is a valuable technique in data analysis for information-preserving data reduction. This paper describes a feature selection approach for hierarchical clustering based on genetic algorithms using a fitness function that tries to minimize the difference between the dissimilarity matrix of the original feature set and the one of the reduced feature sets. Clustering trees based on reduced feature sets are comparable with those based on the complete feature set. Special measures to favor small reduced feature sets are discussed.

The quality of a clustering of chemical data is determined by a proper choice of distance measures and data transformations. The latter aspect is often neglected and its importance is shown here. It is also shown that the V-shaped data structure that is often obtained in a principal component analysis of chemical data may indicate that the clustering of the raw data can lead to classifications that are not relevant from a chemical point of view and that the log double centering transform should be considered as a possible alternative.

Sequential projection pursuit (SPP) is proposed to detect inhomogeneities (clusters) in high-dimensional analytical data. Such inhomogeneities indicate that there are groups of objects (samples) with different chemical characteristics. The method is compared with principal component analysis (PCA). PCA is generally applied to visually explore structure in high-dimensional data, but is not specifically used to find clustering tendency. Projection pursuit (PP) is specifically designed to find inhomogeneities, but the original method is computationally very intensive. SPP combines the advantages of both methods and overcomes most of their weak points. In this method, latent variables are obtained sequentially according to their importance measured by the entropy index. This involves an optimization step, which is achieved by using a genetic algorithm. The performance of the method is demonstrated and evaluated, first on simulated data sets, and then on near-infrared and gas chromatography data sets. It is shown that SPP indeed reveals more easily information about inhomogeneities than PCA.

A general framework for the automatic alignment of one-dimensional chromatographic signals is presented in this article. The alignment of signals was achieved by explicitly modeling the warping function. Its shape was estimated using a linear combination of several B-spline functions. The coefficients of the spline functions were found in the course of an optimization procedure to maximize the Pearson's correlation coefficient between a target chromatogram and aligned chromatogram(s). The computational requirements of the method are discussed with respect to the correlation optimized warping method, frequently used for the alignment of chromatographic signals. As illustrated with two sets of one-dimensional chromatographic fingerprints, the automatic alignment approach performs well even when non-linear peak shifts need to be corrected. It can be applied in an on-the-fly manner since the alignment of signals is rapid.

In this paper, a method is proposed to select subsets of variables in parallel factor analysis (PARAFAC), such that information in the complete multi-way data set is preserved as much as possible. The information retained is measured by means of the percentage of consensus in Procrustes analysis. The best N -way subset is obtained by applying a genetic algorithm (GA) to optimize the consensus between the subset and the complete N -way data set in order to prevent exhaustive searching. The method was applied to two industrial data sets: a three-way sensory data set and a four-way gas chromatography (GC) data set. The results showed that the proposed method successfully identified structure-bearing variables in both data sets and that it led to better subsets of variables than feature selection based on loadings.

ThepurposeofthestudyistoshowhowtheinterpretationofacomplexmultivariatedataarraycansignificantlybeimprovedbytheapplicationofN-wayprincipalcomponentanalysis(PCA).Twofoodrelatedthree-waydatasetswerestudied;asensoryand a chromatographic data array. The Parafac and the Tucker3 models were applied and results were compared. Both N-waymodels presented here allow visualization of the data structure and give detailed information about the data set, notablyallowing to understand relationships between objects and variables. © 2002 Elsevier Science B.V. All rights reserved. Keywords: N-way PCA; Tucker3 model; PARAFAC model; Maillard reaction 1. IntroductionThe main purpose of exploratory data analysisis to learn about interrelationships between objectsand variables. As data sets are becoming larger andmore complex, visualization is needed to achieve thisaim. A very well known method for visualisationof the data patterns is principal component analysis(PCA). The aim of this study is to show that ap-plying the N-way approach (an extension of PCAto higher orders) can significantly improve visual-isation and interpretation of complex multivariatedata compared to other data analysis methods pre-viously applied to the same datasets [1,2]. Tucker3and PARAFAC models are two of the most popularN-way methods. There are many applications of them

A feature selection method is proposed to select a subset of variables in principal component analysis (PCA) that preserves as much information present in the complete data as possible. The information is measured by means of the percentage of consensus in generalised Procrustes analysis. The best subset of variables is obtained by applying a genetic algorithm (GA) to optimise the consensus between the subset and the complete data set in order to avoid exhaustive searching. The method was evaluated on a standard data set known as the Alate data, and on a high-dimensional industrial gas chromatography (GC) data set. The results showed that the proposed method successfully identified structure-bearing variables in both data sets and that it leads to a better subset of variables than other studied feature selection methods.

This article introduces the Neural-Gas network, a fast neural net-based method for clustering, and shows how it is applied to gas chromatographic patterns of Maillard reaction products. The advantages of Neural-Gas are compared to the K-means clustering method and one of the best-known neural methods for clustering, the Kohonen self-organising maps. Some novel combinations with visualization techniques are also presented.