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Application of Class-Modelling Techniques to Near Infrared data for Food
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Authentication Purposes
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P. Oliveri1, V. Di Egidio2, T. Woodcock3 and G. Downey3
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University of Genoa, Department of Drug and Food Chemistry and Technology, Via Brigata
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Salerno, 13 - 16147 Genoa, Italy
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University of Milan, Department of Food Science and Technology, Via Celoria, 2 - 20133 Milan,
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Italy
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Teagasc, Ashtown Food Research Centre, Ashtown, Dublin 15, Ireland
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Abstract
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Following the introduction of legal identifiers of geographic origin within Europe, methods
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for confirming any such claims are required. Spectroscopic techniques provide a method for rapid
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and non-destructive data collection and a variety of chemometric approaches have been deployed
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for their interrogation. In this present study, class-modelling techniques (SIMCA, UNEQ and
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POTFUN) have been deployed after data compression by principal component analysis for the
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development of class-models for a set of olive oil and honey. The number of principal components,
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the confidence level and spectral pre-treatments (1st and 2nd derivative, standard normal variate)
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were varied, and a strategy for variable selection was tried. Models were evaluated on a separate
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validation sample set. The outcomes are reported and criteria for selection of the most appropriate
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models for any given application are discussed.
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Keywords: food authenticity; class-modelling; chemometrics; NIR; spectroscopy
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1. Introduction
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In recent years, there has been a growing interest among consumers in the safety and
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traceability of food products. In particular there is an increasing focus on the geographical origin of
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raw materials and finished products, for several reasons including specific sensory properties,
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perceived health values, confidence in locally-produced products and, finally, media attention
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(Luykx & Van Ruth, 2008). As a result of these factors, the European Union has recognised and
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supported the differentiation of quality products on a regional basis (Dimara & Skuras, 2003),
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introducing an integrated framework for the protection of geographical origin for agricultural
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products and foodstuffs by specific regulation (EU Regulation 510/2006). This regulation permits
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the application of the following geographical indications to a food product: protected designation of
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origin (PDO), protected geographical indication (PGI) and traditional speciality guaranteed (TSG).
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Traditional analyses for food authentication, based on chemical and physical methods, have
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several drawbacks, the most significant of which are low speed, the necessity for sample pre-
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treatments, a requirement for highly-skilled personnel and destruction of the sample (Tomás-
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Barberán, Ferreres, Garciá-Vuguera, & Tomás-Lorente, 1993; Stefanoudaki, Kotsifaki &
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Koutsaftakis, 1997; Anderson & Smith, 2002; Consolandi et al., 2008). Several fast and non-
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destructive instrumental methods have been proposed to overcome these hurdles. Among them,
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infrared spectroscopy has proven to be a successful analytical method for analyses of a variety of
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food products. In particular, the NIR region (between 750 and 2500 nm), in which vibration and
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combination overtones of the fundamental O-H, C-H and N-H bounds are the main recordable
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phenomena (William & Norris, 2001), gives useful spectral fingerprints of food samples.
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In the literature, there are several studies reporting the use of NIR spectroscopy to determine
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geographical and varietal origin of olive oil (Galtier et al., 2007; Casale, Casolino, Ferrari & Forina,
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2008; Sinelli, Casiraghi, Tura & Downey, 2008), wine (Cozzolino, Smyth & Gishen, 2003; Liu et
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al., 2008), honey (Toher, Downey & Murphy, 2007; Woodcock, Downey, Kelly & O’Donnell,
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2007) and other products (Reid, O’Donnell & Downey, 2006). In all these cases, multivariate data
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analysis has been shown to be indispensable for the extraction of the maximum useful information
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from recorded signals.
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In most of the applications found in the literature which report discrimination on the basis of
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geographical origin, classification techniques like linear discriminant analysis (LDA) and partial
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least squares discriminant analysis (PLS-DA) have been used. Given a number of samples
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belonging to some pre-defined classes, classification techniques build a delimiter between these
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classes and always assign each object to the category to which it most probably belongs even in the
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case of objects which are actually extraneous to the classes studied. These methods are not the best
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approach for the verification of food geographical origin, not least because normally there is only a
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single class of interest e.g. a single PDO. In such cases, class-modelling techniques can be properly
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and more appropriately applied (Forina, Casale & Oliveri, 2009; Marini, Bucci, Magrì & Magrì,
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2010); in fact, they provide an answer to the general question: “Is sample X, stated to be of class A,
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really compatible with the class A model?”. This is essentially the question to be answered in
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addressing problems of food geographical authenticity: if a product is sold with a specific claim on
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a label regarding provenance, it is important to be able to verify compatibility of its measured
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characteristics with those of authentic similar material from the declared origin (Forina, Oliveri,
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Lanteri & Casale, 2008).
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A class model is characterised by two parameters: sensitivity and specificity. However,
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when a class-modelling technique such as SIMCA is applied in food authentication, attention is
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often focused only on its classification performance (e.g. correct classification rate). Use of such a
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restricted focus under-utilises the significant characteristics of class-modelling approach.
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The aim of this work is the exploration of three different class modelling techniques
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(SIMCA, UNEQ and POTFUN) to evaluate their abilities for verifying the declared geographical
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origin of two PDO food products: olive oil from Liguria and honey from Corsica. They represent
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economically-valuable food products traded extensively internationally and differing widely in
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composition.
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These sample sets were collected as part of the EU-funded TRACE project
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(http://www.trace.eu.org) and their authenticity is guaranteed. In the case of the olive oil samples,
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classification techniques have previously been applied to the NIR spectral collection and the results
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published (Woodcock, Downey & O’Donnell, 2008).
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2. Materials and Methods
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2.1 Samples and NIR analysis
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Olive oil samples (n= 913) were collected from a number of different areas in Europe over a
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period spanning three harvests: 2005 (316 samples: 63 samples from Liguria and 253 from other
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regions), 2006 (352 samples: 79 samples from Liguria and 273 from other regions) and 2007 (245
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samples: 68 samples from Liguria and 177 from other regions). Oils were sourced from
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Mediterranean countries i.e. Italy, Spain, France, Greece, Cyprus and Turkey (Table 1). All oils
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were transported to a single laboratory (Joint Research Centre, Ispra, Italy) for sub-sampling and
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delivery by air to Ashtown Food Research Centre. Uniquely, oils from harvest 2 (2006) were
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collected and distributed in two separate batches. All olive oils were stored in a refrigerated room (4
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ºC) in the dark between delivery and spectral acquisition (less than 2 weeks), minimising the chance
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of any significant chemical change occurring during this time-period. Olive oil samples (50 ml
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approx.) were placed in screw-capped vials in a water-bath maintained at 30 °C and allowed to
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equilibrate for 30 minutes prior to spectral acquisition. Transflectance spectra (1100-2498 nm) at 2
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nm intervals (700 variables) of each sample were collected. Full experimental details have been
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previously described in Woodcock et al. (2008). Figure 1.a shows an example of NIR spectra of
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olive oil samples.
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Artisanal unfiltered honey samples were collected directly from beekeepers during harvest
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2006 (111 samples from Corsica and 71 from other regions). All honey collected were stored in the
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dark in screw-cap jars at room temperature (18-25 °C) between collection and spectral acquisition
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(less than 2 weeks). Immediately prior to spectral collection, honey samples were incubated at 40
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°C overnight in an air oven and manually stirred to ensure homogeneity. The solids content of each
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sample was measured using a benchtop Abbé model 2WA (Kernco Instruments, Texas, USA)
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refractometer and each sample was adjusted to a standard solids content (70 ±1 °Brix) with distilled
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water. This step was necessary to minimise spectral complications arising from naturally-occurring
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variations in sugar concentration and to avoid spurious classifications on the basis of solids content
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variations between honey samples.
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Before being scanned, honey samples (50 ml approx.) were placed in screw-capped vials in
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a water-bath maintained at 30 °C for 30 minutes. Spectral data were collected in transflectance
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mode (1100-2498 nm) at 2 nm intervals (700 variables) were collected. Full experimental details
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have been previously described in Woodcock, Downey, Kelly & O’Donnell (2007).
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2.2 Data pre-processing
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Spectral data of olive oil and honey were exported from The Unscrambler binary files in
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ASCII format and imported into the chemometric package V-PARVUS (Forina, Lanteri, Armanino,
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Casolino, Casale & Oliveri, 2008).
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Olive oil spectra were structured in a data matrix with 913 rows (samples) and 700 columns
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(variables). A calibration sample set was constructed so as to include equal numbers of Ligurian
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and non-Ligurian oils, i.e. to be balanced with regard to sample type. Two-thirds (n=140) of the
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Ligurian samples were selected at random from the 3-year harvest collection as were an equal
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number of non-Ligurian oils to form a calibration set of 280 samples. All the remaining samples
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were used as an external validation sample set.
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Honey spectra were structured in a matrix with 182 rows (samples) and 700 columns
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(variables). The calibration sample set was constructed by selecting at random two-thirds of the
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total sample set; all of the remaining samples were used as an external validation sample set.
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To remove or at least minimise any unwanted spectral contribution arising from e.g. light
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scatter (Blanco & Pagés, 2002), the effect of a number of mathematical pre-treatments was
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investigated for all models. These pre-treatments included 1st and 2nd derivative using the Savitzky-
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Golay method (Alciaturi, Escobar & De La Cruz, 1998; Vaiphasa, 2006) with cubic smoothing and
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segment sizes between 5 and 21 datapoints, and the standard normal variate (SNV) transform
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(Barnes, Dhanoa & Lister, 1989).
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2.3 Class-modelling techniques
The modelling techniques used in this work were SIMCA (soft independent modelling of
class analogy), UNEQ (unequal class spaces) and POTFUN (potential function techniques).
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2.3.1 Soft Independent Modelling of Class Analogy (SIMCA)
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SIMCA (Wold & Sjöström 1977) was the first class-modelling technique used in
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chemometrics; the central feature of this method is the application of principal component analysis
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(PCA) to the sample category studied (e.g. a PDO food product), generally after within-class
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autoscaling or centering. SIMCA models are defined by the range of the sample scores on a selected
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number of low-order principal components (PCs) and models therefore correspond to rectangles
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(two PCs), parallelepipeds (three PCs) or hyper-parallelepiped (more than three PCs) referred to as
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the SIMCA inner space. Conversely, the principal components not used to describe the model
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define the outer space, considered as uninformative space. The scores range can be enlarged or
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reduced, depending mainly on the number of samples, to avoid the possibility of under- or over-
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estimation (Forina & Lanteri, 1984). The standard deviation of the distance of the objects in the
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calibration set from a model is the class standard deviation. The boundaries of SIMCA space around
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the model are determined by a critical distance, which is obtained by means of Fisher statistics;
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there is no specific hypothesis other than that this distance should be normally distributed.
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However, the distribution of samples in the inner space should be more-or-less uniform otherwise
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regions in the inner space lacking objects from the modelled class would be incorrectly considered
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as a part of the model. Figure 2 shows an example of non-uniform sample distribution in a space
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defined by the first two PCs: in such a case SIMCA is clearly a not satisfactory device (Fig. 2.a), as
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this model includes a large number of objects not belonging to the modelled class.
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SIMCA is a very flexible technique since it allows variation in a large number of parameters
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such as scaling or weighting of the original variables, number of components, expanded or
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contracted scores range, different weights for the distances from the model in the inner space and in
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the outer space and confidence level applied.
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2.3.2 UNEQual class spaces (UNEQ)
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UNEQ, originating in the work of Hotelling (1947), was introduced into chemometrics by
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Derde & Massart (1986). This technique derives from QDA (quadratic discriminant analysis); it is
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based on the hypothesis of a multivariate normal distribution in each category studied and,
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consequently, on the use of T2 statistics to define a class space. The UNEQ model is the centroid i.e.
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the vector of the mean values of the variables. UNEQ should be applied in cases when the ratio
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between the number of objects in a given category and the number of the variables measured is 3 or
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greater. In cases involving many variables (such as spectral data), it is possible to apply UNEQ
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following a preliminary reduction in variable number by PCA. The boundary of the class space
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around the centroid is an ellipse (two variables), an ellipsoid (three variables) or a hyper-ellipsoid
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(more than three variables). The dispersion of a class space is defined by the critical value of the T 2
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statistics at a selected confidence level. The shape and the orientation of the ellipse depend on the
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correlation between the variables. As was stated for SIMCA, if sample distribution in variable space
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is not uniform, UNEQ may not provide satisfactory results (Fig. 2.b).
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2.3.3 POTential FUNction techniques (POTFUN)
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Potential function techniques were introduced to chemometrics by Coomans & Broeckaert
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(1986). These methods estimate a probability density distribution as the sum of the contributions of
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each single object in the calibration set. Here we used a Gaussian-like contribution, with a
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smoothing coefficient (formally analogous to the standard deviation of the Gaussian probability
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function and evaluated by means a leave-one-out procedure) that is a function of the local density of
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objects: this strategy, known as normal variable-potential, is useful when the underlying
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multivariate distribution is very asymmetric, with wide regions characterised by a very low density
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of objects (Forina, Armanino, Leardi & Drava, 1991). The resulting estimated distribution can be
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very complex, capable of effectively describing non-uniform distributions of samples (Fig. 2.c). The
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boundary of the class space is obtained in this approach by the method of the equivalent
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determinant (Forina et al., 1991) at a selected confidence level.
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2.4 Validation parameters
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Sensitivity, specificity and efficiency were computed in this work to evaluate model
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performance. Sensitivity is defined as the percentage of objects in the external validation set
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belonging to the modelled class which are accepted by the model developed using objects in the
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calibration set. Specificity is the percentage of objects belonging to the other (un-modelled)
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category or categories in the external validation set which are rejected by the model developed
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using objects in the calibration set. A class-modelling technique builds a class space around a
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mathematical class model which is the confidence interval, at a pre-selected confidence level, for
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the class objects: sensitivity is its experimental measure. A decrease in the confidence level for the
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modelled class decreases the sensitivity and increases the specificity of the model. Efficiency has
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been computed in this study as geometric mean of sensitivity and specificity values.
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2.5 Variable selection
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In the case of spectral data, not all wavelengths contribute unique or useful information. The
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elimination of predictors of limited or negligible utility can increase the efficiency of class models
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or make their interpretation simpler. Stepwise decorrelation of variables, introduced by Kowalski &
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Bender (1976) as an algorithm with the name SELECT, was applied to the spectral datasets in this
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study. This algorithm can be used both for classification, class-modelling problems and multivariate
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quantitative calibration. In the case of classification and class-modelling problems, SELECT
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functions by a sequential identification and decorrelation of individual variables in the initial
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variable set. For example, SELECT first identifies a variable with the largest Fisher weight (Wold
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& Sjöström, 1977), a measure of the between-class variance: within-class variance ratio. This first
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selected variable is decorrelated from all the others so that these latter become orthogonal to that
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selected. After decorrelation, the selected variable is set aside from the variable set and the process
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repeated with another identification. This identification and decorrelation procedure continues until
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the decorrelated predictors do not have a significant Fisher weight. Decorrelation is especially
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important in the case of spectral data because contiguous variables are often highly inter-correlated.
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3. Results and discussion
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As is typical with NIR spectra, no difference between spectra of olive oils or honey from
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different regions was detectable by the naked eye (data not shown). However, some indication of
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variability in each spectral dataset may be obtained from a principal component scores plot; these
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are shown for olive oil and honey in Figures 1 (a) and (b) respectively. In the case of olive oils, the
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scores plot on PC1 (accounting for 82% of the variation) and PC2 (accounting for 16% of the
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variation) reveals some clustering behaviour that probably relates to harvest, storage time or
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scanning time. For honey, two phenomena may be seen. The first is a vertical separation between
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samples on the basis of harvest year while the second involves a large dispersion of honeys along
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PC1 in the case of harvest 1. The cause of this latter behaviour is unknown; the separation along
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PC2 may be related to factors relating to each harvest or instrument drift or both.
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Tables 2 and 3 show the parameters used to evaluate class-model performance on the
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relevant external validation set for a number of Ligurian olive oil and Corsican honey models. In
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both cases, the number of principal components was varied over a very large range (from 2 to 20), a
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range which was much larger than the number of significant components. In addition, the
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confidence level of each model was varied between 95% and 80%. Two column pre-treatments
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(column centering and column autoscaling) were applied prior to PCA in order to try to balance the
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influence of the variables and improve model performance. The results reported are those which
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produced the highest percentage efficiency on the external validation set for each data pre-treatment
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and confidence level; they are the best according to the maximum efficiency criterion and generally
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correspond to relatively well-balanced values of specificity and sensitivity. Figure 3 is a graphical
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representation of these results: sensitivity and specificity show, as expected, an overall negative
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correlation. Models represented in the upper left or in lower right corners of these plots are
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characterised by relatively unbalanced parameters.
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In the case of Ligurian olive oil, as shown in Table 2, the three class-modelling techniques
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provided quite similar results although at different confidence levels. The sensitivity and specificity
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values associated with the maximum efficiency varied between 70.0 - 90.0% and 62.2 – 87.7 %,
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respectively. The highest efficiency (84.5 %) was obtained by a SIMCA model involving 9 PCs
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after column-centering and a 2nd derivative (21 datapoints) pre-treatment. Comparable values were
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produced by a number of POTFUN models while UNEQ efficiencies never exceeded 80 %. As
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regards selecting the best model, parameters to be considered in addition to sensitivity, selectivity
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and efficiency include the number of components in each model and the confidence level selected.
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It should be noted that quite large numbers of principal components are included in all of the
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models reported in Table 2, varying from 8/9 in the case of SIMCA up to 13 for some POTFUN
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models. These, however, may be a reflection of the type of problem which is being addressed
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namely trying to differentiate between olive oils from separate geographic areas. While there may
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be some expected differences in terms of varietal composition of oils, chemical differences which
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are detected by near infrared spectroscopy may be expected to be very small and therefore
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represented by sources of variation which require the involvement of high-order principal
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components for their description. It may be useful to examine the performance of models which are
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similar to that producing e.g. the highest efficiency value. Take, for example, the SIMCA model
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with the efficiency value equal to 84.5%. This is derived by a 2nd derivative (21 points) pre-
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treatment but efficiency values for related models produced by 2nd derivative (13 datapoints), 2nd
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derivative (9 datapoints) and 2nd derivative (5 datapoints) are a lot lower at 77.2, 78.4 and 77.0%
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respectively. By way of contrast, there are 3 POTFUN models producing percentage efficiency
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values around 83% i.e. 1st derivative (5 datapoints), 1st derivative (9 datapoints) and 1st derivative
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(13 datapoints). These results were also achieved at a higher % confidence level (95% vs 90%),
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which is preferable. POTFUN models can fit data of this type, which exhibit a complex sample
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distribution, better than SIMCA. For this reason, POTFUN results are quite constant when model
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parameters are varied, as it is evident from an inspection of Figure 3-a.
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Sensitivity and specificity percentages for any given model can be altered by varying the
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associated confidence level. A particular example of this is given by POTFUN which, at a 90%
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confidence level and using >12 PCs, produced the high specificity values (more than 90 %), but
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was associated with very low sensitivity figures of between 60 and 70 % (unpublished data).
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Similarly, UNEQ models developed on this olive oil dataset achieved even higher sensitivity values
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(about 97 %) but at the expense of unacceptably low specificity values (<40 %) (results not shown).
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In case of Corsican honey, as shown in Table 3, models produced by UNEQ and POTFUN
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were characterised by similar sensitivity values although UNEQ produced models with the highest
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sensitivity (94.6%). It was notable that sensitivity values for all of the SIMCA models were much
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lower (59.5 to 70%). Regarding specificity values, SIMCA did produce models with very high
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values (between 87 and 100%) while POTFUN and UNEQ produced similar and lower ranges from
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69.6 up to 87.0%. Overall, the highest efficiency (88.4 %) was obtained by UNEQ and involved a
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model using 6 PCs, a 2nd derivative (9 points) pre-treatment and an 85% confidence level. POTFUN
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also produced models with high efficiency around 83%. Since the results of SIMCA are very
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unbalanced with regard to sensitivity and specificity values, as clearly shown in Figure 3-b, SIMCA
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models cannot be considered appropriate for this data set.
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Applying the criteria discussed above, it may be that the model with best performances
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figures at a high (95%) confidence level and a low (4) number of principal components involves
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POTFUN using a 1st derivative (5 or 9 datapoints) pre-treatment.
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Efficiency values achieved by SIMCA and POTFUN varied between 75.4 – 82.2 % and 75.1
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– 84.0 %, respectively. Also in the case of honey, with a proper combination of number of PCs and
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confidence level, UNEQ and POTFUN can provide high-sensitivity models (close to 100 %) but
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these are associated with very low specificity values (data not shown).
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In food authentication problems, both sensitivity and specificity are important. Sensitivity
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near to 100 % means that almost all samples produced and controlled by e.g. the PDO Corsican
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honey consortium are accepted by the model built for this class; associated high specificity values
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mean that almost all non-Corsican samples are rejected. Depending on the particular aim, therefore,
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it is possible and maybe even desirable to choose models characterised by elevated values of either
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or both of these parameters. For example, from the viewpoint of a national regulatory body, a model
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with 100% sensitivity and specificity is the goal since all compliant and non-compliant samples will
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be correctly identified. However, in the case of a marketing body, the most important criterion for a
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good model may be that it identifies all of the samples produced in e.g. a given PDO as being
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compliant with the model for samples from that PDO. Such a model does not mean that samples
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originating outside the region will, in all cases, be classified outside the model but that is not of
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prime importance in this case.
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Variable selection using the SELECT algorithm was applied two both olive oil and honey
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spectral datasets with the aim of removing uninformative variables and thereby potentially
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improving model sensitivity and specificity. The results showed sensitivity and specificity values
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very close to those obtained using the full variable dataset. In this case, therefore, variable reduction
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did not significantly improve percentage efficiency results. For example, the best POTFUN models
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for honey data after variable reduction achieved a maximum efficiency (1st derivative 5 pts) of 85.8
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% versus 83.2 % obtained previously when all variables were retained. The explanation for this may
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be that all models were developed using principal components, which extract the maximum useful
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information available in the spectral data. It may also be, of course, that the information used in
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model development is dispersed throughout the entire spectral range.
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Classification results for these sample sets and issues have been previously published
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(Woodcock et al., 2008; Woodcock et al., 2009). With regard to olive oils, the best PLS-DA models
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correctly identified the origins of 92.8 and 81.2% of Ligurian and non-Ligurian samples in a
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prediction sample set respectively. In the case of honeys, correct classification rates of 90.4 and
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86.3% for Corsican and non-Corsican prediction samples respectively were reported. It is difficult
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to make meaningful comparisons between these results and those of the class-models developed in
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the current study but it is fair to say that class-modelling methods produced correct classification
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rates similar to those achieved by PLS-DA and have a firmer theoretical basis. Given that the
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classification approach depends on the development of two models (e.g. Ligurian olive oil and non-
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Ligurian olive oil) and that the composition of the latter class cannot be well-defined, PLS-DA
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models will always be heavily influenced by the composition of this sample class.
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4. Conclusions
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Class-modelling methods are appropriate for addressing problems of the type that typically
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arise in food authentication studies. In this study, models have been developed for olive oil and
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honey, each from a single PDO region in Italy and France respectively. Different options with
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regard to the identification of the most appropriate or best model have been discussed. Arising from
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this discussion, models with sensitivity percentages of up to 90% for Ligurian olive oil (UNEQ) and
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94.6% for Corsican honey (UNEQ) may be selected. Using overall percentage efficiency as an
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indicator of success, best models for both Ligurian olive oil and Corsican honey were developed by
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a potential function technique (POTFUN) and produced values of around 83%.
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Acknowledgements
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Thanks are due to the EU-funded TRACE project for the samples and to T. Woodcock for
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collecting the spectral data. The information contained in this article reflects the authors’ views; the
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European Commission is not liable for any use of the information contained therein.
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445
446
447
448
449
450
451
18
(a)
452
(b)
453
454
455
Figure 1. Principal component scores (PC1 vs PC2) plots of all samples of (a) olive oil and (b)
456
honey.
457
19
458
459
460
461
Fig. 2. Lines represent SIMCA (a), UNEQ (b) and POTFUN (c) models based on the first two PCs
in a simulated example for non-uniformly distributed objects. (filled squares: objects belong to the
modelled class, open squares: objects are extraneous to it)
20
462
463
464
465
466
467
468
469
470
Fig. 3. Representation of the results, in terms of sensitivity and specificity on the external validation
set, for models of Ligurian olive oil (a) and Corsican honey (b), as reported in Tables 1 and 2. (S:
SIMCA models, U: UNEQ models, P: POTFUN models)
21
471
472
Table 1. Sources of olive oil samples
Harvest
Liguria
Italy
Non-Liguria
Greece
Spain
France
Cyprus
Turkey
Total
2005
79
173
46
38
10
6
0
352
2006
63
163
25
42
9
0
14
316
2007
68
116
7
34
20
0
0
245
Total
210
452
78
114
39
6
14
913
473
474
22
475
476
477
Table 2. Ligurian olive oil: best model performances on the external validation set according to the
maximum efficiency criterion
ClassModelling
Technique
SIMCA
UNEQ
POTFUN
Sensitivity
(%)
Specificity
(%)
75.7
82.9
80.0
80.0
71.4
70.0
72.9
71.4
81.4
82.9
85.7
88.6
87.1
87.1
90.0
85.7
87.1
87.1
88.6
90.0
84.2
80.0
80.0
78.6
77.1
75.7
78.6
80.0
72.9
78.6
87.7
77.1
76.6
77.6
78.9
84.7
84.4
83.5
87.7
78.7
67.0
71.2
71.8
72.3
70.2
62.9
66.6
67.7
70.2
68.9
62.2
86.3
86.2
86.9
82.6
74.4
82.1
81.8
84.9
79.6
478
Efficiency
(%)479
480
81.5481
482
79.9483
78.3484
78.8
75.1
77.0
78.4
77.2
84.5
80.8
75.8
79.4
79.1
79.4
79.5
73.4
76.2
76.8
485
78.8486
78.8
72.4487
83.1
488
83.0
82.6489
79.8
75.1490
80.3
80.9491
78.7
492
79.1
493
494
23
495
496
Table 3. Corsican honey: best model performances on the external validation set according to the
497
maximum efficiency criterion
ClassSensitivity Specificity Efficiency
Modelling
(%)
(%)
(%)498
499
Technique
500
78.2
70.2
87.0
501
62.2
100.0
78.8502
80.5503
64.9
100.0
80.5504
64.9
100.0
77.1505
62.2
95.7
SIMCA
78.8
64.9
95.7
78.8
62.2
100.0
77.1
59.5
100.0
75.4
59.5
95.7
82.2
67.6
100.0
89.2
69.6
78.8
81.1
82.6
81.8
78.4
82.6
80.5
78.4
82.6
80.5
81.1
78.3
79.7
UNEQ
94.6
73.9
83.6
94.6
82.6
88.4
86.5
73.9
80.0
89.2
69.6
78.8
86.5
73.9
80.0
83.8
73.9
78.7
83.8
82.6
83.2
83.8
82.6
83.2
81.1
87.0
84.0
75.7
82.6
79.1
POTFUN
83.8
69.6
76.3
75.7
87.0
81.1
73.0
82.6
77.6
81.1
69.6
75.1
86.5
78.3
82.3
24