A STATISTICAL TEST OF CONSENSUS OBTAINED FROM GENERALIZED PROCRUSTES ANALYSIS OF SENSORY DATA

Matrix matching techniques such as Generalized Procrustes Analysis (GPA) always produce a matrix of maximal agreement which can then be used to graphically represent samples in “consensus plots”. The degree to which the consensus plots produced by GPA on sensory data (such as that obtained from free choice profiling) actually give a picture of true consensus among panelists, as opposed to being merely artifacts of the analysis, has not been examined. Using a Monte Carlo approach, a statistical test is defined for qualifying this consensus. Examples of the application of the test to sensory profiling data of fruit flavors are given.     

EVALUATION OF PANELIST PERFORMANCE IN DESCRIPTIVE PROFILING OF RANCID SAUSAGES: A MULTIVARIATE STUDY

This paper illustrates an application of principal component analysis (PCA), partial least squares regression (PLS) and generalized procrustes analysis (GPA) to evaluate the ability of a trained group of assessors to perceive rancidity in foods. PCA and regression PLS were utilized to determine to which extent sensory attributes capture the information perceived by a trained sensory panel, and if this can be developed into a predictive model for rancidity in sausages. The data were submitted to a GPA to obtain a map of the products for each subject as compared with a consensus products map. Assessors plots for the sensory attributes were also obtained to reveal the dissimilarities between panelists and to explore clustering.     

DESCRIPTION OF THE SENSORY CHARACTERISTICS OF SPANISH UNIFLORAL HONEYS BY FREE CHOICE PROFILING

Different Spanish unifloral honeys (eucalyptus, sunflower, rosemary, thyme, lavender, citrus, anise, quercus, and lemon blossom) and one multifloral honey were studied by Free-Choice Profiling (FCP) analysis. Generalized Procrustes Analysis (GPA) applied to the FCP data allowed discrimination between samples and provided information on the attributes responsible for the differences observed. The honeys had significantly different sensory characteristics. Textural attributes were the predominant factor in discriminating between samples, and appearance (color included) was also correlated with GPA dimensions to a lesser extent.     

IDENTIFYING ASSESSOR DIFFERENCES IN WEIGHTING THE UNDERLYING SENSORY DIMENSIONS

In a previous paper Kunert and Qannari (1999) discussed a simple alternative to Generalized Procrustes Analysis to analyze data derived from a sensory profiling study. After simple pretreatments of the individual data matrices, they propose to merge the data sets together and undergo Principal Components Analysis of the matrix thus formed. On the basis of two data sets, it was shown that the results slightly differ from those obtained by means of Generalized Procrustes Analysis.
In this paper we give a mathematical justification to this approach by relating it to a statistical regression model. Furthermore, we obtain additional information from this method concerning the dimensions used by the assessors as well as the contribution of each assessor to the determination of these dimensions. This information may be useful to characterize the performance of the assessors and single out those assessors who downweight or overweight some dimensions. In particular, those assessors who overweight the last dimensions should arouse suspicion regarding their performance as, in general, the last dimensions in a principal components analysis are deemed to reflect random fluctuations.     

FREE CHOICE PROFILING OF CHILEAN GOAT CHEESE

Different goat cheeses from Chile were studied by Free-Choice Profile (FCP) analysis. Generalized Procrustes Analysis (GPA) applied to FCP data permitted differentiation between samples and informed on the attributes responsible for the observed differences. Appearance was a dominant factor in discriminating samples and to a lesser degree textural variables were also correlated with GPA dimensions. In acceptability the fresh cheeses were significantly preferred over the ripened ones.     

ASSOCIATION OF STRAWBERRY YOGURT SENSORY PROPERTIES WITH PRODUCT COMPOSITION BY PROCRUSTES ANALYSIS

The flavor of eight samples of commercial strawberry yogurt was studied by Free-Choice Profile analysis (FCP). Generalized Procrustes Analysis (GPA) applied to FCP allowed differentiation between samples and highlighted flavor attributes responsible for the observed differences. The relation between sensory and physicochemical datasets was studied by means of GPA. Those samples with higher carbohydrate content were perceived as sweeter, having stronger strawberry flavor, and with more dairy and yogurt flavors. Samples with higher titratable acidity, ash and protein content were perceived as more acidic and higher in intensity of "faulty" or "defective" flavors. Higher moisture content was associated with lower intensity of "dairy" flavors (creamy, dairy, and yogurt) and greater intensity of rancid flavor. It is concluded that, though not often used to this end, GPA is a suitable method to study the relationship of sensory and instrumental measurements.     

Time-oriented hierarchical method for computation of principal components using subspace learning algorithm

Principal Component Analysis (PCA) and Principal Subspace Analysis (PSA) are classic techniques in statistical data analysis, feature extraction and data compression. Given a set of multivariate measurements, PCA and PSA provide a smaller set of "basis vectors" with less redundancy, and a subspace spanned by them, respectively. Artificial neurons and neural networks have been shown to perform PSA and PCA when gradient ascent (descent) learning rules are used, which is related to the constrained maximization (minimization) of statistical objective functions. Due to their low complexity, such algorithms and their implementation in neural networks are potentially useful in cases of tracking slow changes of correlations in the input data or in updating eigenvectors with new samples. In this paper we propose PCA learning algorithm that is fully homogeneous with respect to neurons. The algorithm is obtained by modification of one of the most famous PSA learning algorithms--Subspace Learning Algorithm (SLA). Modification of the algorithm is based on Time-Oriented Hierarchical Method (TOHM). The method uses two distinct time scales. On a faster time scale PSA algorithm is responsible for the "behavior" of all output neurons. On a slower scale, output neurons will compete for fulfillment of their "own interests". On this scale, basis vectors in the principal subspace are rotated toward the principal eigenvectors. At the end of the paper it will be briefly analyzed how (or why) time-oriented hierarchical method can be used for transformation of any of the existing neural network PSA method, into PCA method.     

SENSORY PROFILING WITH PROBABILISTIC MULTIDIMENSIONAL SCALING

Variability is a fundamental characteristic of sensory profile data. Ignoring the variability may result in biased solutions that cannot be improved by the collection of additional data. Probabilistic multidimensional scaling (PMDS) models provide a means of accounting for the variability inherent in sensory data by using distributions, instead of points, to portray sensory objects. For profile data with high levels of variability, the probabilistic model recovers latent structure parameters very well — traditional deterministic MDS models and principal components analyses (PCA) do not. Advantages of the PMDS models include their parsimony, testability and extensibility. Two particularly attractive PMDS attributes are their ability to relate consumers' expressions of liking to product profiles and their ability to estimate a product's " perceptual share" from liking and profile data. Used as a criterion with what-if modeling, perceptual share estimates enable the evaluation of alternative product development strategies.     

MULTIVARIATE ANALYSIS OF CONVENTIONAL PROFILING DATA: A COMPARISON OF A BRITISH AND A NORWEGIAN TRAINED PANEL

Many studies have shown that conventional profiling provides reproducible and meaningful results. However, comparison of the technique as used in different countries appears to be nonexistent. In addition, data analysis is often approached differently, and this aspect is also addressed. This paper describes a study to compare the results obtained from profiling milk chocolate samples, using trained panels in Britain and Norway. Data were analyzed using principal component analysis, generalized Procrustes analysis and partial least squares regression. Results indicate that the underlying perceptual structure of the sample spaces obtained from both panels were similar, however, the emphasis on the underlying sensory dimensions differed. Moreover, it was possible to calibrate the two profiles, which has implications for marketing products for export, as well as providing a potential tool for panel monitoring and calibration across cultures.     

Evaluation and Discrimination of Soy Sauce by Computer Analysis of Volatile Profiles

The relationships between gas chromatographic (GC) profiles and sensory data of 72 purely fermented soy sauce samples were analyzed by multiple regression analysis and principal component analysis (PCA). Prior to the analysis, GC data was transformed into 7 different modes in order to compare the fitting to a hypothetical linear model. The result from logarithmically transformed ratio of each peak to the sum of whole peaks showed the best precision of predictability for sensory score (R = 0.978). As the result of PCA, eigen values of 10 PCs were shown to be larger than 1.0 but the 5 major PCs could account for 66% of the variance in the total variance of 39 GC peaks. The first and second PCs showed great importance for aroma quality and similarity or dissimilarity in profiles of extracted PCs showed a similar trend with quality differences evaluated by sensory tests. These results showed the importance of the harmonious balance of each aroma compound to create a preferable soy sauce aroma.     

Principal components analysis of protein structure ensembles calculated using NMR data

One important problem when calculating structures of biomolecules from NMR data is distinguishing converged structures from outlier structures. This paper describes how Principal Components Analysis (PCA) has the potential to classify calculated structures automatically, according to correlated structural variation across the population. PCA analysis has the additional advantage that it highlights regions of proteins which are varying across the population. To apply PCA, protein structures have to be reduced in complexity and this paper describes two different representations of protein structures which achieve this. The calculated structures of a 28 amino acid peptide are used to demonstrate the methods. The two different representations of protein structure are shown to give equivalent results, and correct results are obtained even though the ensemble of structures used as an example contains two different protein conformations. The PCA analysis also correctly identifies the structural differences between the two conformations.     

Sensory evaluation of acids by free-choice profiling

The technique of free-choice profiling was applied in orderto characterize the sensory properties of some common organicand inorganic acids. Analysis of panelists' scores by generalizedProcrustes Analysis (GPA) provided information on the relationshipsamong samples and assessors for both the consensus and individualconfigurations. Results indicated that on a weight basis (w/vor v/v), acids differed in their flavor and taste dynamics.Acids were described differently by individual panelists. The GPA resulted in three important principal axes (PA). Thefirst PA had astringency/mouthfeel as the most important factor,while bitterness and sourness were the most important for thesecond and the third PAs, respectively. At 0.08% (w/v or v/v),the inorganic acids, hydrochloric and phosphoric, were moreastringent than sour. The bitterness of succinic (S) was intenseas was the sourness of fumaric, malic and the combinations offumaric:malic (FM), citric:malic (CM) and citric:fumaric (CF).The sensory characteristics of adipic and quinic were perceivedto be very weak at this concentration. The relationship betweenastringency and pH was more evident than was the relationshipbetween pH and sourness.     

Monitoring of an antigen manufacturing process

Fluorescence spectroscopy in combination with multivariate statistical methods was employed as a tool for monitoring the manufacturing process of pertactin (PRN), one of the virulence factors of Bordetella pertussis utilized in whopping cough vaccines. Fluorophores such as amino acids and co-enzymes were detected throughout the process. The fluorescence data collected at different stages of the fermentation and purification process were treated employing principal component analysis (PCA). Through PCA, it was feasible to identify sources of variability in PRN production. Then, partial least square (PLS) was employed to correlate the fluorescence spectra obtained from pure PRN samples and the final protein content measured by a Kjeldahl test from these samples. In view that a statistically significant correlation was found between fluorescence and PRN levels, this approach could be further used as a method to predict the final protein content.     

Parallel Analysis: a method for determining significant principal components

Abstract. Numerous ecological studies use Principal Components Analysis (PCA) for exploratory analysis and data reduction. Determination of the number of components to retain is the most crucial problem confronting the researcher when using PCA. An incorrect choice may lead to the underextraction of components, but commonly results in overextraction. Of several methods proposed to determine the significance of principal components, Parallel Analysis (PA) has proven consistently accurate in determining the threshold for significant components, variable loadings, and analytical statistics when decomposing a correlation matrix. In this procedure, eigenvalues from a data set prior to rotation are compared with those from a matrix of random values of the same dimensionality (p variables and n samples). PCA eigenvalues from the data greater than PA eigenvalues from the corresponding random data can be retained. All components with eigenvalues below this threshold value should be considered spurious. We illustrate Parallel Analysis on an environmental data set. We reviewed all articles utilizing PCA or Factor Analysis (FA) from 1987 to 1993 from Ecology, Ecological Monographs, Journal of Vegetation Science and Journal of Ecology. Analyses were first separated into those PCA which decomposed a correlation matrix and those PCA which decomposed a covariance matrix. Parallel Analysis (PA) was applied for each PCA/FA found in the literature. Of 39 analy ses (in 22 articles), 29 (74.4 %) considered no threshold rule, presumably retaining interpretable components. According to the PA results, 26 (66.7 %) overextracted components. This overextraction may have resulted in potentially misleading interpretation of spurious components. It is suggested that the routine use of PA in multivariate ordination will increase confidence in the results and reduce the subjective interpretation of supposedly objective methods.