**2.5 Simplex mixture system**

The dataset of binary mixtures was built with a simplex approach [20] where the studied factors were the proportions of the components. FTIR-ATR spectral data of GG and LBG powders were combined in several proportions given by Scheffé's mixture design [21, 22] to create artificial blends. Considering q components and a constant constraint on the sum of component proportions, Scheffé used a regular (q − 1) dimensional simplex to describe the experimental region of the possible component combinations. In our case, a binary system (q = 2), the required simplex is a straight line, where q apexes of simplex space corresponded to pure component (GG or LBG). On this linear space, each of the *N* calculated mixtures was characterized by a weight (wj*)* satisfying the following equations:

$$\sum\_{j=1}^{q=2} \mathbf{w}\_j = \mathbf{1} \tag{6}$$

$$\begin{aligned} \text{height (w}\_{\text{j}} \text{ satisfying the following equations:}\\ \sum\_{\substack{\mathbf{q}=2\\ \mathbf{j}=1}}^{\mathbf{q}=2} \mathbf{w}\_{\mathbf{j}} &=\mathbf{1} \\\\ \mathbf{N} &= \frac{(\mathbf{w} + \mathbf{q} - \mathbf{1})!}{(\mathbf{q} - \mathbf{1})! \mathbf{w}!} \\\\ \text{which is an } \mathbf{q} \text{ and } \mathbf{p} \text{ and } \mathbf{q} \text{, respectively.} \end{aligned} \tag{7}$$

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**Figure 4.**

*Molecular structure of LBG (a) and GG (b) from [14].*

*Discrimination by Infrared Spectroscopy: Application to Micronized Locust Bean and Guar Gums*

of wj. These average mixture profiles were used as input data to perform a linear discriminant analysis to build a calibration model to predict further the pair of points (wGG, wLBG) representing the proportions of each gum in the blends.

The Unscrambler Version 10.3 from CAMO (Computer Aided Modeling, Trondheim, Norway) was used to perform chemometric analyses (PCA, PLS, and

Galactomannans are polysaccharides formed by a linear (1-4)-β-D-mannan backbone with a D-galactose side chain (**Figure 4**). On average, GG has a single α-D-galactopyranosyl unit connected by (1–6) linkages to every second main chain unit. In the case of the LBG, unsubstituted or sparingly (1–4) substituted regions of mannopyranose units and regions heavily substituted with α-D-galactopyranosyl

The galactose substitution that influences the intrinsic flexibility of mannan backbone causes solubility differences and controls the rheological properties. The FTIR-ATR signatures of GG and LBG (**Figure 5**) show essentially difference in intensity due to the mannose/galactose ratio and the presence of residual chemical compounds from thermo-mechanical and chemical dehusking pretreatments (remaining germ particles, products of thermal degradation of endosperm, etc.). In GG, the endosperm is composed of 75% of galactomannose and the rest consists of pentosan, protein, pectin, phytin, ash, and dilute acid insoluble residues [5]. High protein content (like albumin,

LDA). The Scheffé approach was developed using MATLAB R2014b.

*DOI: http://dx.doi.org/10.5772/intechopen.87568*

**2.6 Software**

**3. Results and discussion**

**3.1 Spectral signature of GG and LBG**

residues attached by (1–6)-bonds have been observed.

This method favored a uniform distribution of each mixture between the two pure components and made sure that all these immediate neighbors were at the same distance from the latter. The constant w represented here the mesh step.

An approach similar to that developed by Semmar et al. [20] was applied to take into account the variability of the spectral profile of pure components due to different geographic origins or different manufacturing processes. Spectral profiles of pure component were randomly chosen between the dataset of pure GG or LBG samples to obtain an average profile subsequently used to build mixture components. The number of spectral data of pure components was equal to w, defined previously. k iterations (400) of Scheffé's simplex design were carried out to ensure variability in average spectral profiles. A matrix of (N × k) mixtures was obtained with variables corresponding to the spectral wavenumbers and the associated values *Discrimination by Infrared Spectroscopy: Application to Micronized Locust Bean and Guar Gums DOI: http://dx.doi.org/10.5772/intechopen.87568*

of wj. These average mixture profiles were used as input data to perform a linear discriminant analysis to build a calibration model to predict further the pair of points (wGG, wLBG) representing the proportions of each gum in the blends.

## **2.6 Software**

*Modern Spectroscopic Techniques and Applications*

error on the proportion of each gum as follows:

**2.5 Simplex mixture system**

%specificity = true negative \_\_\_\_\_\_\_\_\_\_\_\_\_\_ expected negative × <sup>100</sup> (4)

Linear discriminant analysis (LDA) is the simplest of all possible classification methods that provide a linear transformation of n-dimensional samples into an m-dimensional space (m < n). LDA allowed to develop a model based on predefined classes (GG proportion-LBG proportion) and corresponding FTIR-ATR data of pure gums and gum blends. Here calibration model was built with gum blends generated mathematically from Scheffé's simplex approach (described in the following section) in order to obtain a large number of combinations of gum proportions with different increments (between 0 and 100%) and determine the best fit parameters for classification of gums. These models were then used to classify pure gums or blends not considered in the calibration step. For models, the percentage of recognition (or correct classification) of gum proportions was obtained by calculating first the absolute

Absolute error = |proportionpredicted − proportionreference|guar or locust bean gum (5)

A correct classification was considered when absolute error on gum proportion was inferior to the increment and a value of one was attributed to the sample. Otherwise, a zero value was affected to samples with badly predicted gum propor-

The dataset of binary mixtures was built with a simplex approach [20] where the studied factors were the proportions of the components. FTIR-ATR spectral data of GG and LBG powders were combined in several proportions given by Scheffé's mixture design [21, 22] to create artificial blends. Considering q components and a constant constraint on the sum of component proportions, Scheffé used a regular (q − 1) dimensional simplex to describe the experimental region of the possible component combinations. In our case, a binary system (q = 2), the required simplex is a straight line, where q apexes of simplex space corresponded to pure component (GG or LBG). On this linear space, each of the *N* calculated mixtures was characterized by a weight (wj*)* satisfying the following equations:

> ∑ j=1 q=2

N = \_

This method favored a uniform distribution of each mixture between the two pure components and made sure that all these immediate neighbors were at the same distance from the latter. The constant w represented here the mesh step. An approach similar to that developed by Semmar et al. [20] was applied to take into account the variability of the spectral profile of pure components due to different geographic origins or different manufacturing processes. Spectral profiles of pure component were randomly chosen between the dataset of pure GG or LBG samples to obtain an average profile subsequently used to build mixture components. The number of spectral data of pure components was equal to w, defined previously. k iterations (400) of Scheffé's simplex design were carried out to ensure variability in average spectral profiles. A matrix of (N × k) mixtures was obtained with variables corresponding to the spectral wavenumbers and the associated values

(w + q − 1)! (q − 1)!w!

wj = 1 (6)

(7)

tion. Then a percentage of correct classification was calculated.

**80**

The Unscrambler Version 10.3 from CAMO (Computer Aided Modeling, Trondheim, Norway) was used to perform chemometric analyses (PCA, PLS, and LDA). The Scheffé approach was developed using MATLAB R2014b.
