**5.5. A research example: combined utilization of PCA and PARAFAC on 3D fluorescence spectra to study botanical origin of honey**

#### *5.5.1. Application of PCA*

26 Analytical Chemistry

Practical aspects of PARAFAC modelling of fluorescence

Detection of Active Photosensitizers in Butter

Lagoon of Venice

concentration

(riboflavine, protoporphyrine, hématoporphyrine, chlorophylle a)

Characterizing the pollution produced by an industrial area in the

Monitoring of the photodegradation process of polycyclic aromatic

Quantification of tetracycline in the presence of quenching matrix

Fluorescence Spectroscopy: A Rapid Tool for Analyzing Dairy

Study of pesto sauce appearance and of its relation to pigment

Books and thesis; Scientific papers; Reviews

such as chemicals and food science, medicine and process chemistry.

**Subject Type Technique(s) Year (Ref.)**  Foundations of the PARAFAC procedure: Models and conditions ---- 1970 [*33*] PARAFAC. Tutorial and Applications General 1997 [*39*] Quantification of major metabolites of acetylsalicylic acid Fluorescence 1998 [*40*] Fluorescence of Raw Cane Sugars Fluorescence 2000 [*41*] Determination of chlorophylls and pheopigments Fluorescence 2001 [*42*]

excitation-emission data Fluorescence 2003 [*43*] Evaluation of Two-Dimensional Maps in Proteomics 2D-PAGE imaging 2003 [*44*]

Quantification of sulphathiazoles in honeys Fluorescence 2004 [*46*]

Calibration of folic acid and methotrexate in human serum samples Fluorescence 2007 [*50*] Quantification of sulphaguanidines in honeys Fluorescence 2007 [*51*] Water distribution in smoked salmon RMN 2007 [*52*]

hydrocarbons Fluorescence + HPLC 2007 [*53*]

effect Fluorescence 2008 [*54*]

Products Fluorescence 2008 [*55*] Determination of aflatoxin B1 in wheat Fluorescence 2008 [*56*]

Determination of vinegar acidity ATR- IR 2008 [*58*] Multi-way models for sensory profiling data Sensory analysis 2008 [*59*]

Kinetic study for evaluating the thermal stability of edible oils 1H-NMR 2012 [*28*]

**Table 8.** Bibliography related to PARAFAC and/or Tucker3 models. Theory and applications in areas

Noodles sensory data analysis Physicochemical

fluorescence 2003 [*45*]

fluorescence 2005 [*47*]

fluorescence 2005 [*48*]

+ sensory analysis 2006 [*49*]

analysis 2006 [*32*]

Fluorescence

Physicochemical

Sensory analysis

+ HPLC-UV 2008 [*57*]

and sensory analysis 2011 [*60*]

Evaluation of Processed Cheese During Storage Front face

Evaluation of Light-Induced Oxidation in Cheese Front face

Olive Oil Characterization Front face

The interest for the use of chemometric methods to process chromatograms in order to achieve a better discrimination between authentic and adulterated honeys by linear discriminant analysis was demonstrated by our group previously [*61*]. An extent of this work was to quantify adulteration levels by partial least squares analysis [*62*]. This approach was investigated using honey samples adulterated from 10 to 40% with various industrial bee-feeding sugar syrups. Good results were obtained in the characterization of authentic and adulterated samples (96.5% of good classification) using linear discriminant analysis followed by a canonical analysis. This procedure works well but the data acquisition is a bit so long because of chromatographic time scale. A new way for honey analysis was recently investigated with interest: Front-Face Fluorescence Spectroscopy (FFFS). The autofluorescence (intrinsic fluorescence) of the intact biological samples is widely used in biological sciences due to its high sensitivity and specificity. Such an approach increases the speed of analysis considerably and facilitates non-destructive analyses. The non-destructive mode of analysis is of fundamental scientific importance, because it extends the exploratory capabilities to the measurements, allowing for more complex relationships such as the effects of the sample matrix to be assessed or the chemical equilibriums occurring in natural matrices. For a recent and complete review on the use of fluorescence spectroscopy applied on intact food systems see [*63, 64*]. Concerning honey area, FFFS was directly applied on honey samples for the authentication of 11 unifloral and polyfloral honey types [*65*] previously classified using traditional methods such as chemical, pollen, and sensory analysis. Although the proposed method requires significant work to confirm the establishment of chemometric model, the conclusions drawn by the authors are positive about the use of FFFS as a means of characterization of botanical origin of honeys samples. At our best knowledge, the previous mentioned paper is the first work having investigated the potential of 2D-front face fluorescence spectroscopy to determine the botanical origins of honey at specific excitation wavelengths. We complete this work by adopting a 3D approach of measurements. We present here below the first characterization of three clear honey varieties (Acacia, Lavender and Chestnut) by 3D-Front Face Spectroscopy.

#### *5.5.1.1. Samples*

This work was carried out on 3 monofloral honeys (Acacia: *Robinia* pseudo-acacia, Lavandula: *Lavandula hybrida* and Chestnut: *Castanea sativa*). Honeys were obtained from French beekeepers. The botanical origin of the samples was certified by quantitative pollen analysis according to the procedure of Louveaux et al. [*66*]. An aliquot part of 10 g of the honey samples was stirred for 10min at low rotation speed (50-80 rpm) after slight warming (40°C, for 1h), allowing the analysis of honeys at room temperature by diminishing potential difficulties due to different crystallization states of samples. Honey samples were pipetted in 3 mL quartz cuvette and spectra were recorded at 20 °C.

#### *5.5.1.2. 3D-Fluorescence spectroscopy*

Fluorescence spectra were recorded using a FluoroMax-2 spectrofluorimeter (Spex-Jobin Yvon, Longjumeau, France) mounted with a variable angle front-surface accessory. The incidence angle of the excitation radiation was set at 56° to ensure that reflected light, scattered radiation and depolarisation phenomena were minimised.

PCA: The Basic Building Block of Chemometrics 29

**Figure 11.** *X*(1) is obtained by juxtaposition of front slides of *X*. In the same way, *X*(2) et *X*(3) are obtained

Here are below examples of 3D-Front Face Fluorescence spectra of samples of this study. The chemical composition of honey is studied and known to a large extent for nearly 50 years. The presence of compounds beneficial to health for their antioxidant properties or for other reasons is well known, this is the case of polyphenols [*68-74*] or amino acids [*75-83*], some of them are good fluorophores like polyphenols. Works evoke the interest of using these fluorophores as tracers of the floral origin of honeys. For example, the ellagic acid was used as a tracer of heather honey Calluna and Erica species while hesperitin was used to certify citrus honeys [*84, 85*] and abscisic acid was considered as molecular marker of Australian Eucalyptus honeys [*86*]. Kaempferol was used as marker of rosemary honey as well as quercetin for sunflower honey [*87*]. As polyphenols, aromatic amino acids were used to characterize the botanical origin or to test the authenticity of honey, this is the case of phenylalanine and tyrosine for honey lavender [*88*] and the glutamic acid for honeydew honeys [*81*]. Therefore, recording the overall fluorescence spectrum over a large range of wavelengths allows for taking into account the fluorescence emission of the major chemical components described above. In our case, recorded spectra for Acacia, Lavender and Chestnut honeys are similar for certain spectral regions but differ in others proving the existence of different fluorophores. These chemical characteristics specific of the composition are very useful for the distinction of flower varieties. Recording of 3D fluorescence spectra containing all the emission spectra over a wide range of excitation wavelengths can take into account all the information associated with the fluorophores

respectively by juxtaposition of horizontal and lateral slides of *X*.

*5.5.1.4. Results and discussion* 

present in honeys.

The fluorescence excitation spectra were recorded from 280 nm to 550 nm (increment 4 nm; slits: 3 nm, both at excitation and emission), the fluorescence emission spectra were recorded from 280 to 600 nm, respectively. For each sample, three spectra were recorded using different aliquots.

#### *5.5.1.3. Data Processing and Statistical Analysis*

The computations were performed using the MATLAB environment, version R2007b [Mathworks, Natick, MA, USA] and with the N-way Toolbox [*67*]. Each EEM corresponds to a landscape-matrix. For each succession of fluorescence spectra corresponds a collection of matrices which needs to be processed in a specific arrangement. A cube is usually used to organize landscape-matrices as depicted in the figure 10.

**Figure 10.** Representation of 3 possible types of arrangements for EEM landscapes processing.

From general point of view, processing this type of data arrangement needs two computing methods: a) 3-way methods such as PARAFAC, Tucker3 or Multiway-PCA and b) 2-way methods such as Principal Component Analysis (PCA) and any other bi-linear technique after data cube unfolding. In the first part of this work, the second approach was used: PCA after the *X*(1) unfolding of the data cube as illustrated in figure 11. From general point of view, if *I* is the dimension corresponding to samples, it is interesting to make the unfolding of the cube by keeping this dimension unchanged. One can see that *X*(1) is the unique unfolding that keep the sample dimension unchanged, therefore we took it thereafter for applying PCA.

**Figure 11.** *X*(1) is obtained by juxtaposition of front slides of *X*. In the same way, *X*(2) et *X*(3) are obtained respectively by juxtaposition of horizontal and lateral slides of *X*.

#### *5.5.1.4. Results and discussion*

28 Analytical Chemistry

different aliquots.

applying PCA.

*5.5.1.2. 3D-Fluorescence spectroscopy* 

*5.5.1.3. Data Processing and Statistical Analysis* 

organize landscape-matrices as depicted in the figure 10.

Fluorescence spectra were recorded using a FluoroMax-2 spectrofluorimeter (Spex-Jobin Yvon, Longjumeau, France) mounted with a variable angle front-surface accessory. The incidence angle of the excitation radiation was set at 56° to ensure that reflected light,

The fluorescence excitation spectra were recorded from 280 nm to 550 nm (increment 4 nm; slits: 3 nm, both at excitation and emission), the fluorescence emission spectra were recorded from 280 to 600 nm, respectively. For each sample, three spectra were recorded using

The computations were performed using the MATLAB environment, version R2007b [Mathworks, Natick, MA, USA] and with the N-way Toolbox [*67*]. Each EEM corresponds to a landscape-matrix. For each succession of fluorescence spectra corresponds a collection of matrices which needs to be processed in a specific arrangement. A cube is usually used to

**Figure 10.** Representation of 3 possible types of arrangements for EEM landscapes processing.

From general point of view, processing this type of data arrangement needs two computing methods: a) 3-way methods such as PARAFAC, Tucker3 or Multiway-PCA and b) 2-way methods such as Principal Component Analysis (PCA) and any other bi-linear technique after data cube unfolding. In the first part of this work, the second approach was used: PCA after the *X*(1) unfolding of the data cube as illustrated in figure 11. From general point of view, if *I* is the dimension corresponding to samples, it is interesting to make the unfolding of the cube by keeping this dimension unchanged. One can see that *X*(1) is the unique unfolding that keep the sample dimension unchanged, therefore we took it thereafter for

scattered radiation and depolarisation phenomena were minimised.

Here are below examples of 3D-Front Face Fluorescence spectra of samples of this study. The chemical composition of honey is studied and known to a large extent for nearly 50 years. The presence of compounds beneficial to health for their antioxidant properties or for other reasons is well known, this is the case of polyphenols [*68-74*] or amino acids [*75-83*], some of them are good fluorophores like polyphenols. Works evoke the interest of using these fluorophores as tracers of the floral origin of honeys. For example, the ellagic acid was used as a tracer of heather honey Calluna and Erica species while hesperitin was used to certify citrus honeys [*84, 85*] and abscisic acid was considered as molecular marker of Australian Eucalyptus honeys [*86*]. Kaempferol was used as marker of rosemary honey as well as quercetin for sunflower honey [*87*]. As polyphenols, aromatic amino acids were used to characterize the botanical origin or to test the authenticity of honey, this is the case of phenylalanine and tyrosine for honey lavender [*88*] and the glutamic acid for honeydew honeys [*81*]. Therefore, recording the overall fluorescence spectrum over a large range of wavelengths allows for taking into account the fluorescence emission of the major chemical components described above. In our case, recorded spectra for Acacia, Lavender and Chestnut honeys are similar for certain spectral regions but differ in others proving the existence of different fluorophores. These chemical characteristics specific of the composition are very useful for the distinction of flower varieties. Recording of 3D fluorescence spectra containing all the emission spectra over a wide range of excitation wavelengths can take into account all the information associated with the fluorophores present in honeys.

PCA: The Basic Building Block of Chemometrics 31

Legend: "ACA = Acacia"; "CHA = Chestnut" ; LAV = Lavender

after standardization.

**Figure 13.** Ellipsoids of samples distribution drawn with interval confidence at 95%

**Figure 14.** Loadings on PC1 (at left) and PC2 (at right) computed from EEM cube of honey samples

In the same manner, the loadings on PC2 show two excitation/emission maxima (356/376 nm, 396/470 nm; respectively zones 2 and 3) and one excitation/emission minima (350/450 nm; zone 1). These maxima and minima are not absolute and cannot be assimilate to true concentrations but represent what spectral zones have largely change in intensity and shape throughout the analysed samples. So, loadings are an overall photography of changes in the samples mainly due to their botanical origins. Figure 15 presents an overview of the main fluorophores potentially present in dairy and food products [*63, 93*] and some of them are present in honeys too. Here, the chemical interpretation could be made as following. Based

**Figure 12.** (a): At left, excitation-emission spectra of Acacia samples. At right, excitation-emission spectra of Lavender samples, (b): Excitation-Emission spectra of Chestnut samples

Figure 13 shows the PC1 vs PC2 scores-plot of the honeys dataset. PCA has played his role of data reduction technique by creating new set of axes. One can visualize all samples simultaneously on a simple xy-graph with only the two first principal components without loose of information. The first obvious conclusion is the natural classes of honeys clearly appear on the scores-plot. PC1 accounts for 58.2% of the total variance while PC2 explains 32.6% of the total variance of the initial data set. The Acacia group is separated from Chestnut and Lavender essentially on PC1, while PC2 is more characteristic of the distinction between Acacia + Lavender and Chestnut. The shape and location of fluorescence islets on 3D-spectra are assets in the distinction of samples as they relate to the chemical compounds that distinguish the groups. It is important to note here that other multivariate techniques exist that could be applied to these data successfully. Particular, the application of the technique ICA (Independent Component Analysis) which is a factorial technique similar to PCA, we would associate with each calculated component a signal having a greater chemical significance. ICA is capable from a mixture of signals to extract mutually independent components explaining more particularly the evolution of a "pure" signal [*89-92*]. In the case presented here, ICA should probably separate more effectively chemical source signals that are causing the observed differences between the honey samples. The chemical interpretation of this result can be assessed using the loadings on PC1 and PC2. As depicted by figure 14, some spectral regions are responsible of these separations observed on the two first axes of PCA. Two excitation/emission maxima (356/376 nm, 468/544 nm) and two excitation/emission minima (350/440 nm, 368/544 nm) are detectable on the PC1 loadings.

Legend: "ACA = Acacia"; "CHA = Chestnut" ; LAV = Lavender

**Figure 12.** (a): At left, excitation-emission spectra of Acacia samples. At right, excitation-emission

Figure 13 shows the PC1 vs PC2 scores-plot of the honeys dataset. PCA has played his role of data reduction technique by creating new set of axes. One can visualize all samples simultaneously on a simple xy-graph with only the two first principal components without loose of information. The first obvious conclusion is the natural classes of honeys clearly appear on the scores-plot. PC1 accounts for 58.2% of the total variance while PC2 explains 32.6% of the total variance of the initial data set. The Acacia group is separated from Chestnut and Lavender essentially on PC1, while PC2 is more characteristic of the distinction between Acacia + Lavender and Chestnut. The shape and location of fluorescence islets on 3D-spectra are assets in the distinction of samples as they relate to the chemical compounds that distinguish the groups. It is important to note here that other multivariate techniques exist that could be applied to these data successfully. Particular, the application of the technique ICA (Independent Component Analysis) which is a factorial technique similar to PCA, we would associate with each calculated component a signal having a greater chemical significance. ICA is capable from a mixture of signals to extract mutually independent components explaining more particularly the evolution of a "pure" signal [*89-92*]. In the case presented here, ICA should probably separate more effectively chemical source signals that are causing the observed differences between the honey samples. The chemical interpretation of this result can be assessed using the loadings on PC1 and PC2. As depicted by figure 14, some spectral regions are responsible of these separations observed on the two first axes of PCA. Two excitation/emission maxima (356/376 nm, 468/544 nm) and two excitation/emission minima

spectra of Lavender samples, (b): Excitation-Emission spectra of Chestnut samples

(350/440 nm, 368/544 nm) are detectable on the PC1 loadings.

**Figure 13.** Ellipsoids of samples distribution drawn with interval confidence at 95%

**Figure 14.** Loadings on PC1 (at left) and PC2 (at right) computed from EEM cube of honey samples after standardization.

In the same manner, the loadings on PC2 show two excitation/emission maxima (356/376 nm, 396/470 nm; respectively zones 2 and 3) and one excitation/emission minima (350/450 nm; zone 1). These maxima and minima are not absolute and cannot be assimilate to true concentrations but represent what spectral zones have largely change in intensity and shape throughout the analysed samples. So, loadings are an overall photography of changes in the samples mainly due to their botanical origins. Figure 15 presents an overview of the main fluorophores potentially present in dairy and food products [*63, 93*] and some of them are present in honeys too. Here, the chemical interpretation could be made as following. Based on PC1, Acacia samples are mainly distinguished from Lavender and Chestnut honeys by fluorophores appearing in zone 1 and 2, their content in these fluorophores are greater than other samples. Symmetrically, Lavender and Chestnut honeys are more characterized by fluorophores detected in zone 3 and 4. Loadings on PC2 allow a better understanding of what is more characteristic of Chestnut honeys samples compared with others. Zone 2 and 3 are clearly associated with Chestnut samples because the loading values are positive in these regions as the scores are for these samples on the corresponding graph.

PCA: The Basic Building Block of Chemometrics 33

heating).The results for mode 1 (emission wavelengths), mode 2 (excitation wavelengths) and mode 3 (samples) are presented below in figures 16 and 17. An interesting parallel between the reconstructed PCA loadings and the PARAFAC loadings in each three modes is

**Figure 16.** On top left hand side: PCA loadings for component 1; On top right hand side: PARAFAC loadings for Mode 1 (Emission); On bottom left hand side: PARAFAC loadings for Mode 2 (Excitation);

A simultaneous reading of PCA and PARAFAC loadings for honeys EEM matrices gives some elements for understanding what makes distinction between honeys samples on PARAFAC loadings on mode 3. One can see, for example, samples are relatively well separated on the two first PARAFAC loadings in mode 3 (chart on the bottom right). We find good agreement between the PARAFAC profiles and loadings of PCA. Similarly with PCA loadings, those of PARAFAC show the greatest variation of concentration profiles across all samples. And negative areas in the PARAFAC profiles reflect a decrease in fluorescence and therefore a decrease in concentration of the compounds across all the samples. Complementarily, positive PARAFAC profiles indicate an increase in fluorescence and thus the concentration of the corresponding fluorescent compounds in the samples. The first PARAFAC component in mode 3 (chart on the bottom right) allows a good discrimination of the honey samples and the latter is mainly explained by the variation of the fluorescence depicted by the loading 1 (red line) both on the emission (at top and right hand side) and excitation (at bottom and left hand side) graphs. Therefore, Acacia samples have lower content in these compounds than lavender honey samples. Chestnut honeys

On bottom right hand side: PARAFAC loadings for Mode 3 (Samples)

possible by forming the good figure arrangement.

**Figure 15.** On Left - Excitation and emission maxima of fluorophores present in dairy products (from [*93*]); On right - Fluorescence landscape map indicating the spectral properties of the selected 11 foodrelevant fluorophores (from [*63*]).

#### *5.5.2. Application of PARAFAC*

Let us to consider the previous example on the analysis of three varieties of monofloral honeys. The application of the PARAFAC model (with orthogonality constraint on the 3 modes) to the 3-way EEM fluorescence data can take into account the nature of these trilinear data and get factorial cards similarly to PCA. In the case of PARAFAC, it is usual to identify modes of the PARAFAC model from the dimensions of the original data cube. In our case, we built the cube of fluorescence data as *HoneyCube* = [151 x 91 x 32] which is [em x ex x samples].

Therefore, according to the theoretical model presented above we are able to visualize as many factorial cards as components couples in each mode there are. It is particularly interesting in the case of mode 3 which is mode of samples. The user must specify the number of components in each mode that must be calculated in the model. We built a 3 components model by helping us with the *corcondia* criterion associated with the PARAFAC procedure. The *corcondia* criterion was created and used [*94*] to facilitate the choice of the optimal number of components in the calculated model. It is a number between 0% (worst model fitting) and 100% (best model fitting). The ideal case for choosing the optimal number of components should be to know the exact number of fluorescence sources in the samples, but in our case this number is unknown. We have consider three sources of fluorescence according to our knowledge of the samples (proteins and free amino acids, NADH from cellular materials and oxidation products + Maillard reaction fluorescent products from heating).The results for mode 1 (emission wavelengths), mode 2 (excitation wavelengths) and mode 3 (samples) are presented below in figures 16 and 17. An interesting parallel between the reconstructed PCA loadings and the PARAFAC loadings in each three modes is possible by forming the good figure arrangement.

32 Analytical Chemistry

relevant fluorophores (from [*63*]).

ex x samples].

*5.5.2. Application of PARAFAC* 

on PC1, Acacia samples are mainly distinguished from Lavender and Chestnut honeys by fluorophores appearing in zone 1 and 2, their content in these fluorophores are greater than other samples. Symmetrically, Lavender and Chestnut honeys are more characterized by fluorophores detected in zone 3 and 4. Loadings on PC2 allow a better understanding of what is more characteristic of Chestnut honeys samples compared with others. Zone 2 and 3 are clearly associated with Chestnut samples because the loading values are positive in

**Figure 15.** On Left - Excitation and emission maxima of fluorophores present in dairy products (from [*93*]); On right - Fluorescence landscape map indicating the spectral properties of the selected 11 food-

Let us to consider the previous example on the analysis of three varieties of monofloral honeys. The application of the PARAFAC model (with orthogonality constraint on the 3 modes) to the 3-way EEM fluorescence data can take into account the nature of these trilinear data and get factorial cards similarly to PCA. In the case of PARAFAC, it is usual to identify modes of the PARAFAC model from the dimensions of the original data cube. In our case, we built the cube of fluorescence data as *HoneyCube* = [151 x 91 x 32] which is [em x

Therefore, according to the theoretical model presented above we are able to visualize as many factorial cards as components couples in each mode there are. It is particularly interesting in the case of mode 3 which is mode of samples. The user must specify the number of components in each mode that must be calculated in the model. We built a 3 components model by helping us with the *corcondia* criterion associated with the PARAFAC procedure. The *corcondia* criterion was created and used [*94*] to facilitate the choice of the optimal number of components in the calculated model. It is a number between 0% (worst model fitting) and 100% (best model fitting). The ideal case for choosing the optimal number of components should be to know the exact number of fluorescence sources in the samples, but in our case this number is unknown. We have consider three sources of fluorescence according to our knowledge of the samples (proteins and free amino acids, NADH from cellular materials and oxidation products + Maillard reaction fluorescent products from

these regions as the scores are for these samples on the corresponding graph.

**Figure 16.** On top left hand side: PCA loadings for component 1; On top right hand side: PARAFAC loadings for Mode 1 (Emission); On bottom left hand side: PARAFAC loadings for Mode 2 (Excitation); On bottom right hand side: PARAFAC loadings for Mode 3 (Samples)

A simultaneous reading of PCA and PARAFAC loadings for honeys EEM matrices gives some elements for understanding what makes distinction between honeys samples on PARAFAC loadings on mode 3. One can see, for example, samples are relatively well separated on the two first PARAFAC loadings in mode 3 (chart on the bottom right). We find good agreement between the PARAFAC profiles and loadings of PCA. Similarly with PCA loadings, those of PARAFAC show the greatest variation of concentration profiles across all samples. And negative areas in the PARAFAC profiles reflect a decrease in fluorescence and therefore a decrease in concentration of the compounds across all the samples. Complementarily, positive PARAFAC profiles indicate an increase in fluorescence and thus the concentration of the corresponding fluorescent compounds in the samples. The first PARAFAC component in mode 3 (chart on the bottom right) allows a good discrimination of the honey samples and the latter is mainly explained by the variation of the fluorescence depicted by the loading 1 (red line) both on the emission (at top and right hand side) and excitation (at bottom and left hand side) graphs. Therefore, Acacia samples have lower content in these compounds than lavender honey samples. Chestnut honeys

have an intermediate level of concentration concerning these compounds. Figure 17 gives some elements to more accurately identify the chemical origin of the observed differences between samples on the 2nd PARAFAC component (in blue) on mode 3 (samples). Particularly, it is possible to associated to the 2nd PARAFAC component of mode 3 to Maillard and oxidation products (excitation wavelength: ≈360 nm; emission wavelength: ≈445 nm) depicted by the loadings 2 (blue curve) on the excitation and emission loadings graphs. This observation is explained by the method of harvesting, storage and chemical composition of honey. Indeed, lavender honey experienced a hot extraction and uncapping the honey frames also. This is because the lavender honey crystallizes faster than other honeys because of a higher concentration of sucrose while acacia honey is rich in fructose (sugar does not crystallize) and contains no sucrose. The water content and the glucose / fructose ratio of honeys are also important factors in the crystallization process [*95*]. The harvesting method is to cause a greater concentration of oxidation products and products of the Maillard reaction.

PCA: The Basic Building Block of Chemometrics 35

It is clear here that the PARAFAC loadings probably do not reflect pure signals. Indeed, in our case, the appropriate model is probably more complex because we do not know the exact number of fluorophores present in the samples and their contribution is included in each PARAFAC loadings. Thus the chemical interpretation is only partially correct, but nevertheless shows some interesting information on what produces the differences between samples. Another aspect that we have not discussed here is the type of constraint that we have imposed to the model during its construction (orthogonality, non-negativity, unimodality ...). The type of constraints strongly modifies the shape of the PARAFAC loadings obtained and their comparison with PCA is not always possible. We preferred the orthogonality constraint to be in conditions similar to PCA. But this is not necessarily the best choice from spectroscopic point of

view, particularly because loadings reflecting concentrations should not be any negative.

If there were one or two things to note from this application of PARAFAC, it would be, first, the simplicity of the graphical outputs and their complementarities with the results of PCA, and secondly, the possibility offered by the model to process data inherently 3-way or more

In the case of 3D fluorescence data, the loadings of PCA are not easily used directly to interpret and to construct a model of quantitative monitoring, PARAFAC modelling enables this by producing as much as possible loadings representative of changes in concentrations of fluorophores present in the samples, and a good distinction of the studied honey varieties

Here is below a selection of the most interesting books dealing with chemometrics. This list

Härdle, W.; Simar, L., *Applied multivariate statistical analysis*. 2nd ed.; Springer: Berlin;

Brereton, R. G., *Chemometrics for pattern recognition*. Wiley: Chichester, U.K., 2009; p xvii,

Gemperline, P., *Practical guide to chemometrics*. 2nd ed.; CRC/Taylor & Francis: Boca

Miller, J. N.; Miller, J. C., *Statistics and chemometrics for analytical chemistry*. 5th ed.;

Beebe, K. R.; Pell, R. J.; Seasholtz, M. B., *Chemometrics : a practical guide*. Wiley: New

Pearson Prentice Hall: Harlow, England; New York, 2005; p xvi, 268 p.

Brown, S. D., Comprehensive chemometrics. Elsevier: Boston, MA, 2009

**5.6. Conclusion** 

**Appendix** 

504 p.

**A. Chemometrics books** 

New York, 2007; p xii, 458 p.

Raton, 2006; p 541 p.

York, 1998; p xi, 348 p.

(without preliminary rearrangement).

is easily achievable with a simple PARAFAC model.

will be convenient as well for the beginner as for the specialist.

**Figure 17.** On top left hand side: PCA loadings for component 2; On top right hand side: PARAFAC loadings for Mode 1 (Emission); On bottom left hand side: PARAFAC loadings for Mode 2 (Excitation); On bottom right hand side: PARAFAC loadings for Mode 3 (Samples)

It is clear here that the PARAFAC loadings probably do not reflect pure signals. Indeed, in our case, the appropriate model is probably more complex because we do not know the exact number of fluorophores present in the samples and their contribution is included in each PARAFAC loadings. Thus the chemical interpretation is only partially correct, but nevertheless shows some interesting information on what produces the differences between samples. Another aspect that we have not discussed here is the type of constraint that we have imposed to the model during its construction (orthogonality, non-negativity, unimodality ...). The type of constraints strongly modifies the shape of the PARAFAC loadings obtained and their comparison with PCA is not always possible. We preferred the orthogonality constraint to be in conditions similar to PCA. But this is not necessarily the best choice from spectroscopic point of view, particularly because loadings reflecting concentrations should not be any negative.

## **5.6. Conclusion**

34 Analytical Chemistry

the Maillard reaction.

have an intermediate level of concentration concerning these compounds. Figure 17 gives some elements to more accurately identify the chemical origin of the observed differences between samples on the 2nd PARAFAC component (in blue) on mode 3 (samples). Particularly, it is possible to associated to the 2nd PARAFAC component of mode 3 to Maillard and oxidation products (excitation wavelength: ≈360 nm; emission wavelength: ≈445 nm) depicted by the loadings 2 (blue curve) on the excitation and emission loadings graphs. This observation is explained by the method of harvesting, storage and chemical composition of honey. Indeed, lavender honey experienced a hot extraction and uncapping the honey frames also. This is because the lavender honey crystallizes faster than other honeys because of a higher concentration of sucrose while acacia honey is rich in fructose (sugar does not crystallize) and contains no sucrose. The water content and the glucose / fructose ratio of honeys are also important factors in the crystallization process [*95*]. The harvesting method is to cause a greater concentration of oxidation products and products of

**Figure 17.** On top left hand side: PCA loadings for component 2; On top right hand side: PARAFAC loadings for Mode 1 (Emission); On bottom left hand side: PARAFAC loadings for Mode 2 (Excitation);

On bottom right hand side: PARAFAC loadings for Mode 3 (Samples)

If there were one or two things to note from this application of PARAFAC, it would be, first, the simplicity of the graphical outputs and their complementarities with the results of PCA, and secondly, the possibility offered by the model to process data inherently 3-way or more (without preliminary rearrangement).

In the case of 3D fluorescence data, the loadings of PCA are not easily used directly to interpret and to construct a model of quantitative monitoring, PARAFAC modelling enables this by producing as much as possible loadings representative of changes in concentrations of fluorophores present in the samples, and a good distinction of the studied honey varieties is easily achievable with a simple PARAFAC model.
