**3.4 Quantitative analysis of gum mixtures**

*Modern Spectroscopic Techniques and Applications*

*SEC or SEP: standard error of calibration or prediction, R<sup>2</sup>*

The calibration model had very good quality parameters, as shown in **Table 3**, and very good validation results for LBG were obtained using normalized spectra with

**Model parameters Values** Spectra number for calibration 150 Spectra number for validation 147 LV 3 SEC 0.08 SEP 0.11 R2 0.97 Q2 0.94 %Sensibility 100 %Specificity 100 %Correct classification 100

 *or Q2*

For GG validation, the different statistic parameters were also closed to 100%. The following graph (**Figure 10**) shows that predicted values from validation

Calibration model has satisfying quality parameters, as shown in **Figure 10**, with

classification is obtained. The predicted species origins are never given by zero or one results because the different rates of carbohydrates in the samples vary according to the origins. As a matter of fact, there is a natural variation of the carbohydrate rates that can notably be a function of geographic origins and harvest dates. Contrary to the results of Prado et al. [12] who published that diffuse reflectance (DRIFT) method was better suited for differentiation of gum type, ATR technique

realized spectra with a ZnSe multiple bounce ATR on gum aqueous solutions, heated for their preparation. Nevertheless, the work of Wang et al. [14] showed that the computer-simulated molecular space filling structure of GG and LBG was different in no solvent and aqueous environments. In the aqueous environment, GG form presented a more complicated structure than LBG form because of the increase in galactose units on the mannose backbone [14]. In conclusion, spectral data in solid or liquid environment were difficult to compare as done by Prado et al. [12] because the

showed here a very good classification. It was noted that these authors have

intermolecular interactions in the structure of gums were not the same.

.

(R-square), and 100% good

 *correlation coefficients for calibration or prediction.*

a selection of wavelength region from 1450 to 700 cm<sup>−</sup><sup>1</sup>

*Predicted versus reference value of gum classification (validation step).*

data are closed to zero for GG and 1 for LBG.

RMSEP ranging from 0.11 for LBG to 0.94 for Q2

**86**

**Figure 10.**

**Table 3.**

*PLS-1-DA parameters for LBG.*

As PLS-DA allowed easily the prediction of the botanical origin of galactomannans, LDA was adapted to the prediction of the proportions (or weights, wi) of pure compounds in blends with the advantage to be governed by a constant sum of wj (equal to 100%). But the fact to provide ordinal predictions (or class) leads to a strict response of model, which considers a wrong classification even if the predictive weights are slightly different from reference data. A selection of variables between 1900 and 650 cm<sup>−</sup><sup>1</sup> and an average reduction (by two) of variables in this spectral zone were performed to make simplex iterative operations possible, and because in LDA classification method, the number of objects (or pairs of weights) should be larger than the number of variables (wavenumbers). In this way, 325 variables, 11 pairs of weights between 0 and 1 (with a constant increment of 0.1), and a value of *k* (number of iterations in Scheffé's simplex) equal to 400 to be superior at the variable number (the constraint of LDA calibration step) were used to generate 4400 artificial bends (11 × 400) from simplex design.

An example of the repartition of simulated blends generated with this method is given in **Figure 11** where a step of 10% was chosen to clarify the graphic representation. The graph has been obtained after realizing a PCA on blends' binary data.

Dispersed experimental samples were placed at the extrema of PC1 axis: LBG at the left in the negative part of PC1 and GG at the right in the positive part, respectively. It well appears that simulated blends well take into account the intrinsic variability of pure components, but in certain regions, an inevitable overlapping originating from the high variability of chemical composition of pure gums is also observed.

Five different LDA calibration models were built with five values of weight step (0.100, 0.050, 0.04, 0.02, and 0.007). The robustness of each calibration model has been tested with four validation sets obtained with steps of 0.10, 0.083, 0.067, and 0.002, without constraint about the number of blends. The results are resumed in **Table 4**.

All weights of GG and LBG in pure state and mixtures containing 2–10% of GG were well predicted in the validation step. A percentage of 61% was obtained when the increment chosen in validation was lower than the calibration step.

**Figure 11.** *Location of the binary blends in the simplex space defined by GG and LBG proportions (step of 10%).*


**Table 4.**

*Prediction of correct weight for different validation sets.*
