Detection and Quantification of Goat Milk Adulteration Using FT-NIR Spectroscopy combined with Partial Least Squares and Logistic Regression

Detection and Quantification of Goat Milk Adulteration Using FT-NIR Spectroscopy combined with Partial Least Squares and Logistic Regression | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Detection and Quantification of Goat Milk Adulteration Using FT-NIR Spectroscopy combined with Partial Least Squares and Logistic Regression Paula Giarolla Silveira, Clara Mariana Gonçalves Lima, Dariush Khademi Shurmasti, and 6 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6801468/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Goat milk is a nutrient-rich food and due to its higher commercial value, it is not uncommon for it to be adulterated by the addition of water and cow milk. In this work, ternary mixtures of goat milk, cow milk and water were analyzed by FT-NIR(S), PLS and Logistic Regression. Exploratory investigation showed three ranges of spectral values most strongly associated with separation between the mixtures analyzed, 10800 to 9800, 8800 to 7200 and 6400 to 5600 cm − 1 . The PLS models showed good predictive capacity to quantify the percentages of water, goat milk and cow milk in the ternary mixtures over a wide range of values. Logistical Regression was also good at classifying samples into two adulteration groups. FT-NIR spectroscopy, together with multivariate techniques, proved to be very promising as an analytical methodology for the rapid identification of adulteration and economic fraud in goat milk. Authenticity Multivariate modeling Mixture PLS Logistic Regression Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction For many regions worldwide, goat milk production is deeply intertwined with local customs and dietary patterns. Goat milk is valued for its high digestibility, reduced allergenic potential, and nutritional profile, being rich in proteins, calcium, and essential vitamins. Its utility spans numerous dairy products, including cheese, yogurt, ice cream, kefir, and ricotta (Kapadiya et al., 2016 ; Sumarmono, 2022 ). Owing to its biochemical similarity to human milk, goat milk is often better tolerated than cow milk, leading to fewer allergic and gastrointestinal issues (Li et al., 2024 ). Despite representing a smaller share of global milk production compared to cow or buffalo milk, goat milk holds substantial economic and dietary significance, particularly in countries such as India, Sudan, and France (Teixeira et al., 2021 ). In South America, Brazil leads in goat milk production, generating around 26 million liters annually across nearly 15,700 farms, with intensification expanding in the southern regions (Oliveira et al., 2022 ). However, the premium market value of goat milk makes it vulnerable to adulteration, often through dilution with water or the addition of cheaper bovine milk, which not only compromises product integrity but also poses health risks (Li et al., 2024 ). Incidents such as the 2008 melamine contamination in China underscore the public health threats of milk adulteration, reinforcing the importance of rigorous quality control and detection methodologies. In Brazil, such practices are explicitly prohibited under the Normative Instruction No. 37/2000 by the Ministry of Agriculture (Chen et al., 2017 ; MAPA, 2000). To address adulteration, a variety of analytical techniques have emerged. These include polymerase chain reaction (PCR) (Li et al., 2024 ; Sarkar et al., 2024 ), enzyme-linked immunosorbent assay (ELISA), and High Performance Liquid Chromatography (HPLC), which are widely used to detect foreign proteins or DNA (Chi et al., 2024 ; Eldahshoury & Hurley, 2023 ; Li et al., 2023 ). More advanced methods like matrix-assisted laser desorption ionization mass spectrometry (MALDI-MS) (Tehrani et al., 2024 ), biosensors (Shalileh et al., 2023 a; Shalileh et al., 2023 b), electronic nose combined with machine learning (Tian et al., 2023 ), photoacoustic spectroscopy (Sharifi et al., 2023 ), Raman spectroscopy combined with support vector machine (Ni et al., 2023 ), multi-spectral image, fluorescence and infrared spectroscopy (Boukria et al., 2023 ) are also gaining prominence. As an alternative, Near-Infrared (NIR) spectroscopy has proven to be a rapid, non-destructive, and cost-effective analytical method for food analysis, as well as a fast and easy-to-use technique widely applied in the analysis of agricultural products, foodstuffs, environmental waste, and biomedicine (Lima et al., 2025 ; Yuan et al., 2023 ; Pereira et al., 2021 ; Pereira et al., 2020 ). The principle of this technique is based on the interaction between infrared light and the molecules of the material to be analyzed, in a range of wave-lengths from 780 to 2500 nanometers, and when interacting with the light, the molecules will vibrate at specific frequencies in this range. In this way, certain types of chemical bonds, such as C-H, N-H and O-H can be readily identified in NIR spectra by comparing them with spectra of reference substances (Siesler et al., 2002 ; Ciurczak et al., 2021 ). Despite growing interest in NIR techniques, few studies have evaluated their effectiveness in detecting multiple adulterants in goat milk, particularly when combined with accessible statistical models such as Partial Least Squares (PLS) and Logistic Regression (RegLog). This gap highlights the need for new tools capable of rapidly identifying and quantifying adulteration in routine quality control. In this work, NIR spectroscopy was used, together with classical multivariate analysis methods, to detect and quantify the adulteration of goat milk in ternary mixtures composed of water, cow milk and goat milk, in different proportions. A RegLog was used in order to classify the samples into two possible groups, fraudulent milk and SNSF (sample not suspected of fraud). The experimental hypothesis here is that this regression makes it possible to adequately identify adulterated samples, while the PLS technique makes it possible to quantify the percentage of goat milk in the samples considered by RegLog to be adulterated. 2. Material and Methods 2.1 Milk samples Samples of raw cow milk were provided by the Milk and Derivatives Laboratory of the Food Science Department of the Federal University of Lavras (UFLA, MG, Brazil). A total of three liters of cow milk, cooled to 4°C, were used to create a representative mixture of different milkings and animals of various breeds. The goat milk samples were provided by the Capril Eldorado farm (Perdões, MG, Brazil) and arrived at the laboratory frozen. They were thawed and kept at 4°C until the analyses were carried out. Three liters of raw goat milk were used, forming a representative mixture of different milkings and production batches. 2.2 Experimental design and physicochemical characterization of samples 2.2.1 Experimental design The experimental design consisted of ternary mixtures with different proportions of water, cow milk and goat milk, as shown in Fig. 1 (a). These mixtures were prepared in test tubes containing a total volume of 10.0 ml, and were kept under refrigeration until the time of analysis. In Fig. 1 (a), the nodes highlighted in red correspond to repetitions of the experiment (n = 2). Physicochemical characterization analyses were carried out on the goat milk and cow milk, while FT-NIR spectroscopy was performed on all the ternary mixtures. The spectra were discretized and the data obtained was used to carry out descriptive statistical analyses using the SAS OnDemand statistical package (SAS Institute Inc., 2014). Principal component analysis, preference mapping, partial least squares regression (PLS) and correlation analysis were carried out using the same software. Orange Data Mining software (Demšar et al., 2013 ) was used to perform the logistic regression (RegLog). RegLog was used to identify adulterated samples, classifying them as samples not suspected of fraud (SNSF) and fraudulent samples, while PLS was used to quantify the percentage of goat milk present in the sample. 2.2.2 Physicochemical characterization of samples The following physicochemical properties were used to characterize the samples: pH Measurements were performed in duplicate using a digital benchtop pH meter (PHB-550, Incotherm) with automatic temperature compensation. For the pure milk samples (cow and goat), titration curves were constructed by gradually adding volumes of 0.1 N NaOH (from 0.0 to 6.0 mL) and recording the corresponding pH values. Titulatable acidity Determined by volumetric titration using 0.1 N NaOH, standardized with potassium biphthalate, and phenolphthalein as the indicator. Analyses were conducted in duplicate, following the procedures described in standard food analysis protocols (Zenebon et al., 2008 ). Relative desity The relative density of milk at 15‰ was measured using a Quevenne lactodensimeter, according to the methodology used by Zenebon et al. ( 2008 ). Relative density analyzes were performed in triplicate. Solid content The percentage of solids-not-fat (SNF) in the milk was determined using an optical Brix refractometer (Alba Electronics Ltda.), calibrated with distilled water and operating in the 0–32% Brix range. Measurements were performed in duplicate following the standard methodology (Zenebon et al., 2008 ). Electric conductivity The electrical conductivity of the milk samples was analyzed in duplicate using a portable conductivity meter with automatic temperature compensation (KR30, Akrom Products), in accordance with standard procedures. Total fat To determine the total amount of fat in milk samples, the Gerber butyrometer method, described by Britz & Robinson ( 2008 ), was used. Fat analyzes were performed in duplicate. Cryoscopy The cryoscopic index of the milk samples was measured in a digital electronic cryoscope (MK 540 Flex II Bancada ITR, Instrumentos para Laborato´rios TR Ltda ME) according to the methodology cited by Britz & Robinson ( 2008 ). Relative viscosity The electronic circuit in Fig. 1 (b) is a very low-cost (< $ 10) resource used to accurately measure the flow time of milk in a 50.0 ml burette. The flow time was used to calculate the relative viscosity of milk (η), according to the methodology described by Sorrell ( 1971 ). The data acquisition system in this Figure was directly connected to the soundcard of a PC desktop running Linux Mint 64 Bits, i5 processor and 8 MB of RAM. Audacity free software ((Audacity Team, 2014) GNU GPL) was used to measure the flow time, with error < 0.45 s (n = 6). The circuit in Fig. 1 (b) has eight 1N4148 diodes, two 5 kΩ trimpots, two 10 kΩ resistors, a stereo P2 plug, two photodiodes, two infrared emitting LEDs, two 1 kΩ resistors, two 4.7 kΩ resistors and a 5 Vdc (200 mA) power supply. 2.3 NIR spectroscopy The ternary mixtures corresponding to each node in Fig. 1 (a) were analyzed on an FT-NIR spectrometer operating in diffuse reflectance mode (FT-NIR Bruker, model MPA, Bruker Optik GmbH, Ettlingen, Germany), with Opus software, version 7.5. The spectra were obtained in the range between 12000 and 4000 cm − 1 , with 32 scans per sample and a spectral resolution of 8 cm − 1 . 3. Results and Discussion 3.1. Sample characterization data Table 1 shows the physicochemical properties of the goat milk and cow milk used in the experiments. Table 1 Physicochemical properties of goat and cow milk used in the experiments ( n = 2). Physicochemical property of milk Milk Unit Cow Goat Apparent pH 6.72 ± 0.15 6.68 ± 0.12 – Tritrable acidity 0.16 ± 0.01 0.15 ± 0.01 % LA Relative density 1.033 ± 0.001 1.033 ± 0.001 – Solid content 9.8 ± 0.2 9.8 ± 0.2 g/ 100 g Electric conduct. 4.25 ± 0.05 4.64 ± 0.05 mS/cm Total fat 3.8 ± 0.1 4.3 ± 0.1 g/ 100 g Cryoscopy − 0.543 ± 0.001 − 0.575 ± 0.001 ‰ Relative viscosity (1.081 ± 0.035) × 10 − 3 (1.055 ± 0.047) × 10 − 3 Pa.s All physicochemical properties evaluated were within the expected ranges reported in the literature. The average reference pH value is 6.70 for both types of milk. However, as pH measurement only applies to dilute aqueous solutions and for a narrow range of temperatures (Buck et al., 2002 ), in this work, the pH was called ’apparent pH’, and this is justified by the fact that milk has a complex chemical composition and cannot be considered as a dilute aqueous solution. The apparent pH in Table 1 should therefore only be used for comparative purposes with milk quality measurements made by other authors. These results confirm that the milk samples were of satisfactory quality for subsequent analysis. The effect of freezing goat milk on its chemical composition was disregarded here. According to Wilson et al. (2012), in a study of milk from Saanen goats at different stages of lactation, freezing did not cause any changes in the percentage values of its main constituents (Pinto Junior et al., 2012 ). 3.2 Titration curves and NIR spectroscopy data analysis The titration curves in Fig. 2 (a) show differences in the chemical compositions of goat milk and cow milk, and this is due to both the types and quantities of compounds that react or are neutralized by the addition of NaOH. These compounds include Na + , K + , Ca 2+, Mg 2+ , Cl − , PO 3− , SO 2− , HCO − , citrate-ion, Fe 3+ , Cu 2+ , Sn 2+ , Al 3+ , Zn 2+ , Co 2+ , Mn 2+ , F − , Br − , casein, albumin and dissolved carbon dioxide, among others (Spreer, 2017 ). These differences in chemical composition, especially the ionic fraction, suggested that FT-NIR could be used as an analytical methodology to detect the adulteration of goat milk (Wang et al., 2004 ). In Fig. 2 (a) the derivative curves indicate the apparent pH ranges in which there are the greatest variations in the titration curves. Figure 2 (b) shows the FT-NIR spectra of the ternary mixtures. In the samples with higher percentages of water, the spectra of samples with high water content—particularly pure water, differ significantly from those containing milk, with samples identified more clearly in the PCA of Fig. 2 (d), and which are located at the bottom left. The ternary mixtures with higher percentages of milk are grouped closer to the center of Fig. 2 (d). It can therefore be concluded that using FT-NIR it is possible to identify goat milk with different percentages of water and cow milk and thus identify adulterated samples. According to Mehrotra ( 2000 ), fat in raw milk is associated with vibrations at the following wavelengths: C-H at 5800.46 cm − 1 (1 st overtone), C-H at 5707.76 cm − 1 (1st overtone), C-H at 4332.76 cm − 1 (bend 2nd overtone) and C-H2 at 4266.21 cm − 1 (bend 2nd overtone). The protein shows N-H/amide 2nd or N-H/amide 3rd or combination vibrations at 4878.05 cm − 1 and N-H bend 2nd overtone and C-H stretch/C = O stretch combination and C = O stretch/amide 3rd combination at 4587.16 cm − 1 . Lactose shows O-H combination a 4775.55 cm − 1 . Figure 1 (c) was obtained by calculating the correlation between the intensity values of the signals in the FT-NIR spectra at each wavelength and the percentages of goat milk, cow milk and water, as shown in Eq. 1 . $$\:\left(\begin{array}{c}\begin{array}{ccc}{\lambda\:}_{1}&\:{\lambda\:}_{2}\dots\:&\:{\lambda\:}_{m}\\\:{X}_{11}&\:{X}_{12}\dots\:&\:{X}_{1m}\\\:{X}_{21}&\:{X}_{22}\dots\:&\:{X}_{2m}\end{array}\\\:⋮\\\:\begin{array}{ccc}{X}_{n1}&\:{X}_{n2}\dots\:&\:{X}_{nm}\end{array}\end{array}\right)\underrightarrow{\mathbb{R}:n\times\:m}\begin{array}{c}\%\:Goat\:milk\\\:\left(\begin{array}{c}{Y}_{1}\\\:{Y}_{2}\\\:⋮\\\:{Y}_{n}\end{array}\right)\begin{array}{c}{S}_{01}\\\:{S}_{02}\\\:⋮\\\:{S}_{n}\end{array}\end{array}$$ 1 In Eq. 1 , each row in the matrix M nm corresponds to a ternary mixture (sample \(\:{S}_{n}\) ), while each column of this matrix corresponds to a particular wavelength \(\:{\lambda\:}_{m}\) . On the right-hand side of Eq. 1 the vector N n contains the percentages of goat milk (percentage of cow milk or water) for each ternary mixture ( \(\:{S}_{n}\) ). Figure 1 (c) shows that the spectral bands at wavelengths above 7000 cm − 1 have higher correlation values with the percentages of goat milk, cow milk and water, and for water, the correlation is negative throughout this wavelength range. This result suggests that the PLS and RegLog prediction models will preferentially use the spectral information contained in this range of values. 3.3 Spectral variance and analysis of preference map data A sample variance calculation was carried out for each wavelength (each column) of the M nm matrix, in Eq. 1 . The aim of this calculation was to check which wavelengths are related to the highest variance values between the different FT-NIR spectra shown in Fig. 1 (b). The hypothesis here is that the wavelengths with the highest variance values are also those with the greatest ability to separate and distinguish between the spectra, since variance is a measure that describes the spread of a variable (Loftus, 2022 ). Figure 3 (a) shows the variance data between the FT-NIR spectra calculated at each wavelength. In Fig. 3 (a) the curve deconvolution of the variance data generated a total of 9 (nine) Gaussians ( R 2 = 0.9903, RMSE = 0.0035876) allowing us to identify the wavelengths that most affect the separation between the samples: 10208.3 cm − 1 , 8636.6 cm − 1 , 8277.23 cm − 1 , 7677.68 cm − 1 , 7465.6 cm − 1 , 7343.12 cm − 1 , 7269.68 cm − 1 , 5948.94 cm − 1 To assess the reliability of FT-NIR spectroscopy in correctly identifying the composition of each ternary mixture, a preference map was made from the infrared spectra (SAS: Proc MD239 Pref; Kuhfeld, 2010 ; SAS Institute Inc., 2014). Figure 3 (b), showing that FT-NIR was able to map the spatial coordinates for each ternary mixture in the experiment quite accurately and clearly reconstructed the same triangular shape shown in Fig. 1 (a). It can thus be confirmed that FT-NIR spectroscopy was able to correctly detect the differences between all the samples analyzed, within a wide range of percentage variation in the mixture of goat milk, cow milk and water. 3.4 Validation and PLS data analysis Partial least squares regression was performed using Proc PLS (SAS OnDemand, SAS Institute Inc., 2014). 20% of the samples were selected for external validation, while the remaining samples (80%) were used for training. A preliminary step was used to remove outliers and extreme values in order to improve the accuracy of the predictor models. A predictor model was obtained for each response variable and the accuracy of these models was assessed using their respective R 2 values, for training and external validation data, as well as an analysis of the graphs obtained by plotting the experimental values versus the values predicted by the models. The results obtained are shown in the graphs in Fig. 4 . The plots in Fig. 4 show that the models obtained had good predictive capacity for a wide range of values for percentages of cow milk, goat milk and water. In addition to the PLS, a backpropagation artificial neural network (ANN) was built in parallel using the Orange Data Mining software (Demšar et al., 2013 ). An ANN was constructed with the objective of simultaneously predicting all components of the ternary mixtures; however, validation errors exceeded 40%, rendering the model unsuitable. However, when PLS was used to generate individual models for each response variable, these were considered good, with good predictive capacity, as shown in Fig. 4 . 3.5 Validation of Logistic Regression model The results of the logistic regression (RegLog) are shown in Table 2 . The RegLog was carried out in order to assess whether the ternary blend samples could be classified into two groups: ’Fraud’, corresponding to samples of goat milk suspected of being adulterated in some way, by adding water, cow milk or both in some proportion. Samples with a percentage of goat milk greater than 9 % would be considered ’SNSF’ (sample not suspected of fraud) by RegLog. Adulteration values of less than 1 % for goat milk were not evaluated, as fraudsters generally prefer to adulterate milk with slightly higher percentages, possibly in order to increase profits. Ali Ahmad (2009) reports 35. % added water and starch in raw milk. Table 2 Confusion matrix used to evaluate the classification performance of Logistic Regression Predicted Training ( n = 60, R 2 = 0.999) Validation ( n = 19, R 2 = 0.947) SNSF Fraud SNSF Fraud Experimental SNSF 2 0 0 1 Fraud 0 58 0 18 Total 2 58 0 19 The confusion matrix in Table 2 shows that for training data, RegLog was able to correctly classify the samples, with R 2 = 0.999. For the validation data, RegLog was also able to make a good classification, although it made a mistake when evaluating a single sample ( R 2 = 0.947). This table shows that there were fewer SNSF samples and this is due to two factors. Firstly, there were far fewer SNSF samples in the data files used for training and validation, justified by the ternary mixture design, in which the samples with the lowest percentage of goat milk adulteration are closer to one of the vertices of the triangle shown in Fig. 1 (a). The other factor is due to the fact that the samples are randomly selected by the RegLog algorithm, and an SNSF sample may or may not be drawn. In the different draws made when carrying out this analysis, it was observed that the result was basically the same, with none or a single sample incorrectly classified by the algorithm. 4. Conclusion FT-NIR spectroscopy, when coupled with multivariate analysis, proved to be an effective method for both detecting and quantifying goat milk adulteration by the addition of water and cow milk, over a wide range of percentage values. Logistic regression was able to detect adulterated goat milk, with R 2 = 0.947 (n = 19), while PLS regression models were able to quantify the percentage of goat milk adulteration with R2 greater than 0.99, both for the addition of water and cow milk. These findings support the potential application of PLS and logistic regression as rapid screening tools for detecting economic fraud in goat milk. Declarations Author Contribution P.G.S. Conceptualization, Methodology, Data Analysis, Writing – original draft. C.M.L. Investigation, Writing - review & editing, Visualization. J.L.C. Investigation, Methodology, Visualization, Resources. C.R.P.S. Investigation, Writing - review & editing, Visualization. D.K.S. Investigation, Writing - review & editing, Visualization. V.C.A. Conceptualization, Writing - original draft, Visualization. M.J.V.B. Conceptualization, Writing - review & editing, Visualization. S.V. Conceptualization, Writing - original draft, Visualization. R.A.R. Project administration, Conceptualization, Funding acquisition, Methodology, Investigation, Data curation, Supervision, Writing - review & editing. References Adam, A. A. H. (2009). Milk adulteration by adding water and starch at Khartoum State. Pakistan Journal of Nutrition , 8(4), 439–440. Boukria, O., Boudalia, S., Bhat, Z. F., Hassoun, A., & Aït-Kaddour, A. (2023). 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The causal-effect model of input factor allocation on maize production: Using binary logistic regression in search for ways to be more productive. Journal of Agriculture and Food Research , 16, 101094. Sarkar, D., Ranjan, R., Marwaha, S., Sahoo, A., & Naha, S. (2024). Multiplex PCR for detection of camel milk adulteration with cattle and goat milk. International Dairy Journal , 154, 105922. SAS Institute Inc. (2014). SAS® OnDemand for Academics: User’s Guide . Cary, NC: SAS Institute Inc. SciDAVis. (2022). Scidavis: Scientific data analysis and visualization [computer program], version 2.9.2. Retrieved from https://scidavis.sourceforge.io/ . Accessed on April 19, 2024. Shalileh, F., Sabahi, H., Dadmehr, M., & Hosseini, M. (2023). Sensing approaches toward detection of urea adulteration in milk. Microchemical Journal , 193, 108990. Shalileh, F., Sabahi, H., Golbashy, M., Dadmehr, M., & Hosseini, M. (2023). 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Rapid identification and quantification of vegetable oil adulteration in raw milk using a flash gas chromatography electronic nose combined with machine learning. Food Control , 150, 109758. Wang, G. Q., Wang, F., Chen, D., Su, Q. D., & Shao, X. G. (2004). A novel method for the determination of inorganic ions in complex plant samples by near infrared spectroscopy. Spectroscopy and Spectral Analysis, 24(12), 1540–1542. Wojdyr, M. (2016). Fityk curve fitting [Computer program]. Version 1.3.1. Retrieved from https://fityk.nieto.pl/ . Accessed on 04/19/2024. Yang, M., Ye, A., Gilbert, E. P., Yang, Z., Everett, D. W., & Singh, H. (2024). Pepsin-induced hydrolysis and coagulation of proteins in goat, sheep and cow milk. International Dairy Journal , 153, 105898. Yasin, N., Naqvi, S. M. D., & Akhter, S. M. (2024). Simultaneous spectrophotometric determination of Co(II) and Co(III) in acidic medium with partial least squares regression and artificial neural networks. Heliyon , 10(4), e26373. Yuan, L., Chen, X., Huang, Y., Chen, J., & Pan, T. (2023). Spectral separation degree method for vis-NIR spectroscopic discriminant analysis of milk powder adulteration. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy , 301, 122975. Zenebon, O., Pascuet, N. S., & Tiglea, P. (2008). Physicochemical Methods for Food Analysis. (4th ed.). 1st Digital Edition. Adolfo Lutz Institute, São Paulo, Brazil. Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6801468","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":465520099,"identity":"89d077e4-21e2-475f-b983-0cc7fb4aa15d","order_by":0,"name":"Paula Giarolla Silveira","email":"","orcid":"","institution":"Federal University of Lavras (UFLA)","correspondingAuthor":false,"prefix":"","firstName":"Paula","middleName":"Giarolla","lastName":"Silveira","suffix":""},{"id":465520100,"identity":"6ca4b1fc-fa5a-44e3-ae98-400ebde375fd","order_by":1,"name":"Clara Mariana Gonçalves 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(UFLA)","correspondingAuthor":false,"prefix":"","firstName":"Roney","middleName":"Alves","lastName":"Rocha","suffix":""}],"badges":[],"createdAt":"2025-06-02 10:53:36","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6801468/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6801468/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83983367,"identity":"fac8a3e2-aad1-45a4-8ba9-5987ef4c63ed","added_by":"auto","created_at":"2025-06-05 10:28:12","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":375391,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6801468/v1/8729e712bc7b84cb44424ff4.png"},{"id":83983365,"identity":"9cb2ba97-8d8d-44b1-84bb-63cd77f662f6","added_by":"auto","created_at":"2025-06-05 10:28:12","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":970516,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6801468/v1/6e4418cfa1d9789fda0ffd04.png"},{"id":83983376,"identity":"2784cdcb-16cb-43e2-a988-9227bbd66cb7","added_by":"auto","created_at":"2025-06-05 10:28:12","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":499714,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6801468/v1/19d233c4316d3d49400b8068.png"},{"id":83983378,"identity":"e6894c28-bda7-477d-a087-c86c0bcd73e1","added_by":"auto","created_at":"2025-06-05 10:28:12","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":927325,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6801468/v1/fd5069521436551e7094fbb4.png"},{"id":83984368,"identity":"55dcb321-a205-4ca5-b421-de8580aab900","added_by":"auto","created_at":"2025-06-05 10:44:14","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3487853,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6801468/v1/3dc813f1-bf57-4091-af4d-483d48a5d4ed.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Detection and Quantification of Goat Milk Adulteration Using FT-NIR Spectroscopy combined with Partial Least Squares and Logistic Regression","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eFor many regions worldwide, goat milk production is deeply intertwined with local customs and dietary patterns. Goat milk is valued for its high digestibility, reduced allergenic potential, and nutritional profile, being rich in proteins, calcium, and essential vitamins. Its utility spans numerous dairy products, including cheese, yogurt, ice cream, kefir, and ricotta (Kapadiya et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Sumarmono, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Owing to its biochemical similarity to human milk, goat milk is often better tolerated than cow milk, leading to fewer allergic and gastrointestinal issues (Li et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eDespite representing a smaller share of global milk production compared to cow or buffalo milk, goat milk holds substantial economic and dietary significance, particularly in countries such as India, Sudan, and France (Teixeira et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In South America, Brazil leads in goat milk production, generating around 26\u0026nbsp;million liters annually across nearly 15,700 farms, with intensification expanding in the southern regions (Oliveira et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eHowever, the premium market value of goat milk makes it vulnerable to adulteration, often through dilution with water or the addition of cheaper bovine milk, which not only compromises product integrity but also poses health risks (Li et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Incidents such as the 2008 melamine contamination in China underscore the public health threats of milk adulteration, reinforcing the importance of rigorous quality control and detection methodologies. In Brazil, such practices are explicitly prohibited under the Normative Instruction No. 37/2000 by the Ministry of Agriculture (Chen et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; MAPA, 2000).\u003c/p\u003e \u003cp\u003eTo address adulteration, a variety of analytical techniques have emerged. These include polymerase chain reaction (PCR) (Li et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Sarkar et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), enzyme-linked immunosorbent assay (ELISA), and High Performance Liquid Chromatography (HPLC), which are widely used to detect foreign proteins or DNA (Chi et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Eldahshoury \u0026amp; Hurley, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Li et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). More advanced methods like matrix-assisted laser desorption ionization mass spectrometry (MALDI-MS) (Tehrani et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), biosensors (Shalileh et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2023\u003c/span\u003ea; Shalileh et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2023\u003c/span\u003eb), electronic nose combined with machine learning (Tian et al., \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), photoacoustic spectroscopy (Sharifi et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), Raman spectroscopy combined with support vector machine (Ni et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), multi-spectral image, fluorescence and infrared spectroscopy (Boukria et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) are also gaining prominence.\u003c/p\u003e \u003cp\u003eAs an alternative, Near-Infrared (NIR) spectroscopy has proven to be a rapid, non-destructive, and cost-effective analytical method for food analysis, as well as a fast and easy-to-use technique widely applied in the analysis of agricultural products, foodstuffs, environmental waste, and biomedicine (Lima et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Yuan et al., \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Pereira et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Pereira et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The principle of this technique is based on the interaction between infrared light and the molecules of the material to be analyzed, in a range of wave-lengths from 780 to 2500 nanometers, and when interacting with the light, the molecules will vibrate at specific frequencies in this range. In this way, certain types of chemical bonds, such as C-H, N-H and O-H can be readily identified in NIR spectra by comparing them with spectra of reference substances (Siesler et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Ciurczak et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eDespite growing interest in NIR techniques, few studies have evaluated their effectiveness in detecting multiple adulterants in goat milk, particularly when combined with accessible statistical models such as Partial Least Squares (PLS) and Logistic Regression (RegLog). This gap highlights the need for new tools capable of rapidly identifying and quantifying adulteration in routine quality control. In this work, NIR spectroscopy was used, together with classical multivariate analysis methods, to detect and quantify the adulteration of goat milk in ternary mixtures composed of water, cow milk and goat milk, in different proportions. A RegLog was used in order to classify the samples into two possible groups, fraudulent milk and SNSF (sample not suspected of fraud). The experimental hypothesis here is that this regression makes it possible to adequately identify adulterated samples, while the PLS technique makes it possible to quantify the percentage of goat milk in the samples considered by RegLog to be adulterated.\u003c/p\u003e"},{"header":"2. Material and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Milk samples\u003c/h2\u003e \u003cp\u003eSamples of raw cow milk were provided by the Milk and Derivatives Laboratory of the Food Science Department of the Federal University of Lavras (UFLA, MG, Brazil). A total of three liters of cow milk, cooled to 4\u0026deg;C, were used to create a representative mixture of different milkings and animals of various breeds. The goat milk samples were provided by the Capril Eldorado farm (Perd\u0026otilde;es, MG, Brazil) and arrived at the laboratory frozen. They were thawed and kept at 4\u0026deg;C until the analyses were carried out. Three liters of raw goat milk were used, forming a representative mixture of different milkings and production batches.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Experimental design and physicochemical characterization of samples\u003c/h2\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003e2.2.1 Experimental design\u003c/h2\u003e \u003cp\u003eThe experimental design consisted of ternary mixtures with different proportions of water, cow milk and goat milk, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a). These mixtures were prepared in test tubes containing a total volume of 10.0 ml, and were kept under refrigeration until the time of analysis. In Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a), the nodes highlighted in red correspond to repetitions of the experiment (n\u0026thinsp;=\u0026thinsp;2). Physicochemical characterization analyses were carried out on the goat milk and cow milk, while FT-NIR spectroscopy was performed on all the ternary mixtures. The spectra were discretized and the data obtained was used to carry out descriptive statistical analyses using the SAS OnDemand statistical package (SAS Institute Inc., 2014). Principal component analysis, preference mapping, partial least squares regression (PLS) and correlation analysis were carried out using the same software. Orange Data Mining software (Demšar et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) was used to perform the logistic regression (RegLog). RegLog was used to identify adulterated samples, classifying them as samples not suspected of fraud (SNSF) and fraudulent samples, while PLS was used to quantify the percentage of goat milk present in the sample.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.2.2 Physicochemical characterization of samples\u003c/h2\u003e \u003cp\u003eThe following physicochemical properties were used to characterize the samples:\u003c/p\u003e \u003cp\u003e \u003cstrong\u003epH\u003c/strong\u003e \u003cp\u003eMeasurements were performed in duplicate using a digital benchtop pH meter (PHB-550, Incotherm) with automatic temperature compensation. For the pure milk samples (cow and goat), titration curves were constructed by gradually adding volumes of 0.1 N NaOH (from 0.0 to 6.0 mL) and recording the corresponding pH values.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eTitulatable acidity\u003c/strong\u003e \u003cp\u003eDetermined by volumetric titration using 0.1 N NaOH, standardized with potassium biphthalate, and phenolphthalein as the indicator. Analyses were conducted in duplicate, following the procedures described in standard food analysis protocols (Zenebon et al., \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2008\u003c/span\u003e).\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eRelative desity\u003c/strong\u003e \u003cp\u003eThe relative density of milk at 15\u0026permil; was measured using a Quevenne lactodensimeter, according to the methodology used by Zenebon et al. (\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). Relative density analyzes were performed in triplicate.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eSolid content\u003c/strong\u003e \u003cp\u003eThe percentage of solids-not-fat (SNF) in the milk was determined using an optical Brix refractometer (Alba Electronics Ltda.), calibrated with distilled water and operating in the 0\u0026ndash;32% Brix range. Measurements were performed in duplicate following the standard methodology (Zenebon et al., \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2008\u003c/span\u003e).\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eElectric conductivity\u003c/strong\u003e \u003cp\u003eThe electrical conductivity of the milk samples was analyzed in duplicate using a portable conductivity meter with automatic temperature compensation (KR30, Akrom Products), in accordance with standard procedures.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eTotal fat\u003c/strong\u003e \u003cp\u003eTo determine the total amount of fat in milk samples, the Gerber butyrometer method, described by Britz \u0026amp; Robinson (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2008\u003c/span\u003e), was used. Fat analyzes were performed in duplicate.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eCryoscopy\u003c/strong\u003e \u003cp\u003eThe cryoscopic index of the milk samples was measured in a digital electronic cryoscope (MK 540 Flex II Bancada ITR, Instrumentos para Laborato\u0026acute;rios TR Ltda ME) according to the methodology cited by Britz \u0026amp; Robinson (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2008\u003c/span\u003e).\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eRelative viscosity\u003c/strong\u003e \u003cp\u003eThe electronic circuit in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (b) is a very low-cost (\u0026lt; \u003cspan\u003e$\u003c/span\u003e10) resource used to accurately measure the flow time of milk in a 50.0 ml burette. The flow time was used to calculate the relative viscosity of milk (η), according to the methodology described by Sorrell (\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1971\u003c/span\u003e). The data acquisition system in this Figure was directly connected to the soundcard of a PC desktop running Linux Mint 64 Bits, i5 processor and 8 MB of RAM. Audacity free software ((Audacity Team, 2014) GNU GPL) was used to measure the flow time, with error\u0026thinsp;\u0026lt;\u0026thinsp;0.45 s (n\u0026thinsp;=\u0026thinsp;6). The circuit in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (b) has eight 1N4148 diodes, two 5 kΩ trimpots, two 10 kΩ resistors, a stereo P2 plug, two photodiodes, two infrared emitting LEDs, two 1 kΩ resistors, two 4.7 kΩ resistors and a 5 Vdc (200 mA) power supply.\u003c/p\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.3 NIR spectroscopy\u003c/h2\u003e \u003cp\u003eThe ternary mixtures corresponding to each node in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (a) were analyzed on an FT-NIR spectrometer operating in diffuse reflectance mode (FT-NIR Bruker, model MPA, Bruker Optik GmbH, Ettlingen, Germany), with Opus software, version 7.5. The spectra were obtained in the range between 12000 and 4000 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, with 32 scans per sample and a spectral resolution of 8 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Sample characterization data\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the physicochemical properties of the goat milk and cow milk used in the experiments.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePhysicochemical properties of goat and cow milk used in the experiments (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003ePhysicochemical\u003c/p\u003e \u003cp\u003eproperty of milk\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eMilk\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eUnit\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCow\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGoat\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eApparent pH\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e6.72\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e6.68\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTritrable acidity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e0.16\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.15\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e% \u003cem\u003eLA\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRelative density\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e1.033\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e1.033\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026ndash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSolid content\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e9.8\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e9.8\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eg/\u003c/em\u003e100 \u003cem\u003eg\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElectric conduct.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e4.25\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e4.64\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003emS/cm\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal fat\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e3.8\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e4.3\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eg/\u003c/em\u003e100 \u003cem\u003eg\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCryoscopy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e\u0026minus;\u003c/em\u003e0.543\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e\u0026minus;\u003c/em\u003e0.575\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026permil;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRelative viscosity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e(1.081\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.035) \u003cem\u003e\u0026times;\u003c/em\u003e 10\u003csup\u003e\u003cem\u003e\u0026minus;\u003c/em\u003e\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e(1.055\u0026thinsp;\u003cem\u003e\u0026plusmn;\u003c/em\u003e\u0026thinsp;0.047) \u003cem\u003e\u0026times;\u003c/em\u003e 10\u003csup\u003e\u003cem\u003e\u0026minus;\u003c/em\u003e\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003ePa.s\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAll physicochemical properties evaluated were within the expected ranges reported in the literature. The average reference pH value is 6.70 for both types of milk. However, as pH measurement only applies to dilute aqueous solutions and for a narrow range of temperatures (Buck et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), in this work, the pH was called \u0026rsquo;apparent pH\u0026rsquo;, and this is justified by the fact that milk has a complex chemical composition and cannot be considered as a dilute aqueous solution. The apparent pH in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e should therefore only be used for comparative purposes with milk quality measurements made by other authors. These results confirm that the milk samples were of satisfactory quality for subsequent analysis. The effect of freezing goat milk on its chemical composition was disregarded here. According to Wilson et al. (2012), in a study of milk from Saanen goats at different stages of lactation, freezing did not cause any changes in the percentage values of its main constituents (Pinto Junior et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2012\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Titration curves and NIR spectroscopy data analysis\u003c/h2\u003e \u003cp\u003eThe titration curves in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (a) show differences in the chemical compositions of goat milk and cow milk, and this is due to both the types and quantities of compounds that react or are neutralized by the addition of NaOH. These compounds include Na\u003csup\u003e+\u003c/sup\u003e, K\u003csup\u003e+\u003c/sup\u003e, Ca\u003csup\u003e2+,\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMg\u003csup\u003e2+\u003c/sup\u003e, Cl\u003csup\u003e\u0026minus;\u003c/sup\u003e, PO\u003csup\u003e3\u0026minus;\u003c/sup\u003e, SO\u003csup\u003e2\u0026minus;\u003c/sup\u003e, HCO\u003csup\u003e\u0026minus;\u003c/sup\u003e, citrate-ion, Fe\u003csup\u003e3+\u003c/sup\u003e, Cu\u003csup\u003e2+\u003c/sup\u003e, Sn\u003csup\u003e2+\u003c/sup\u003e, Al\u003csup\u003e3+\u003c/sup\u003e, Zn\u003csup\u003e2+\u003c/sup\u003e, Co\u003csup\u003e2+\u003c/sup\u003e, Mn\u003csup\u003e2+\u003c/sup\u003e, F\u003csup\u003e\u0026minus;\u003c/sup\u003e, Br\u003csup\u003e\u0026minus;\u003c/sup\u003e, casein, albumin and dissolved carbon dioxide, among others (Spreer, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). These differences in chemical composition, especially the ionic fraction, suggested that FT-NIR could be used as an analytical methodology to detect the adulteration of goat milk (Wang et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). In Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (a) the derivative curves indicate the apparent pH ranges in which there are the greatest variations\u003c/p\u003e \u003cp\u003ein the titration curves.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (b) shows the FT-NIR spectra of the ternary mixtures. In the samples with higher percentages of water, the spectra of samples with high water content\u0026mdash;particularly pure water, differ significantly from those containing milk, with samples identified more clearly in the PCA of Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (d), and which are located at the bottom left. The ternary mixtures with higher percentages of milk are grouped closer to the center of Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (d). It can therefore be concluded that using FT-NIR it is possible to identify goat milk with different percentages of water and cow milk and thus identify adulterated samples.\u003c/p\u003e \u003cp\u003eAccording to Mehrotra (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2000\u003c/span\u003e), fat in raw milk is associated with vibrations at the following wavelengths: C-H at 5800.46 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e (1 st overtone), C-H at 5707.76 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e (1st overtone), C-H at 4332.76 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e (bend 2nd overtone) and C-H2 at 4266.21 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e (bend 2nd overtone). The protein shows N-H/amide 2nd or N-H/amide 3rd or combination vibrations at 4878.05 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and N-H bend 2nd overtone and C-H stretch/C\u0026thinsp;=\u0026thinsp;O stretch combination and C\u0026thinsp;=\u0026thinsp;O stretch/amide 3rd combination at 4587.16 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. Lactose shows O-H combination a 4775.55 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (c) was obtained by calculating the correlation between the intensity values of the signals in the FT-NIR spectra at each wavelength and the percentages of goat milk, cow milk and water, as shown in Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\left(\\begin{array}{c}\\begin{array}{ccc}{\\lambda\\:}_{1}\u0026amp;\\:{\\lambda\\:}_{2}\\dots\\:\u0026amp;\\:{\\lambda\\:}_{m}\\\\\\:{X}_{11}\u0026amp;\\:{X}_{12}\\dots\\:\u0026amp;\\:{X}_{1m}\\\\\\:{X}_{21}\u0026amp;\\:{X}_{22}\\dots\\:\u0026amp;\\:{X}_{2m}\\end{array}\\\\\\:⋮\\\\\\:\\begin{array}{ccc}{X}_{n1}\u0026amp;\\:{X}_{n2}\\dots\\:\u0026amp;\\:{X}_{nm}\\end{array}\\end{array}\\right)\\underrightarrow{\\mathbb{R}:n\\times\\:m}\\begin{array}{c}\\%\\:Goat\\:milk\\\\\\:\\left(\\begin{array}{c}{Y}_{1}\\\\\\:{Y}_{2}\\\\\\:⋮\\\\\\:{Y}_{n}\\end{array}\\right)\\begin{array}{c}{S}_{01}\\\\\\:{S}_{02}\\\\\\:⋮\\\\\\:{S}_{n}\\end{array}\\end{array}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, each row in the matrix M\u003csub\u003enm\u003c/sub\u003e corresponds to a ternary mixture (sample \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{n}\\)\u003c/span\u003e\u003c/span\u003e), while each column of this matrix corresponds to a particular wavelength \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\lambda\\:}_{m}\\)\u003c/span\u003e\u003c/span\u003e. On the right-hand side of Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e the vector N\u003csub\u003en\u003c/sub\u003e contains the percentages of goat milk (percentage of cow milk or water) for each ternary mixture (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{n}\\)\u003c/span\u003e\u003c/span\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (c) shows that the spectral bands at wavelengths above 7000 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e have higher correlation values with the percentages of goat milk, cow milk and water, and for water, the correlation is negative throughout this wavelength range. This result suggests that the PLS and RegLog prediction models will preferentially use the spectral information contained in this range of values.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Spectral variance and analysis of preference map data\u003c/h2\u003e \u003cp\u003eA sample variance calculation was carried out for each wavelength (each column) of the M\u003csub\u003enm\u003c/sub\u003e matrix, in Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The aim of this calculation was to check which wavelengths are related to the highest variance values between the different FT-NIR spectra shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (b).\u003c/p\u003e \u003cp\u003eThe hypothesis here is that the wavelengths with the highest variance values are also those with the greatest ability to separate and distinguish between the spectra, since variance is a measure that describes the spread of a variable (Loftus, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (a) shows the variance data between the FT-NIR spectra calculated at each wavelength. In Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (a) the curve deconvolution of the variance data generated a total of 9 (nine) Gaussians (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.9903, \u003cem\u003eRMSE\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0035876) allowing us to identify the wavelengths that most affect the separation between the samples: 10208.3 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 8636.6 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 8277.23 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 7677.68 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 7465.6 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 7343.12 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 7269.68 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 5948.94 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo assess the reliability of FT-NIR spectroscopy in correctly identifying the composition of each ternary mixture, a preference map was made from the infrared spectra (SAS: Proc MD239 Pref; Kuhfeld, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; SAS Institute Inc., 2014). Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (b), showing that FT-NIR was able to map the spatial coordinates for each ternary mixture in the experiment quite accurately and clearly reconstructed the same triangular shape shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (a). It can thus be confirmed that FT-NIR spectroscopy was able to correctly detect the differences between all the samples analyzed, within a wide range of percentage variation in the mixture of goat milk, cow milk and water.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Validation and PLS data analysis\u003c/h2\u003e \u003cp\u003ePartial least squares regression was performed using Proc PLS (SAS OnDemand, SAS Institute Inc., 2014). 20% of the samples were selected for external validation, while the remaining samples (80%) were used for training. A preliminary step was used to remove outliers and extreme values in order to improve the accuracy of the predictor models. A predictor model was obtained for each response variable and the accuracy of these models was assessed using their respective \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003evalues, for training and external validation data, as well as an analysis of the graphs obtained by plotting the experimental values versus the values predicted by the models. The results obtained are shown in the graphs in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe plots in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e show that the models obtained had good predictive capacity for a wide range of values for percentages of cow milk, goat milk and water. In addition to the PLS, a backpropagation artificial neural network (ANN) was built in parallel using the Orange Data Mining software (Demšar et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). An ANN was constructed with the objective of simultaneously predicting all components of the ternary mixtures; however, validation errors exceeded 40%, rendering the model unsuitable. However, when PLS was used to generate individual models for each response variable, these were considered good, with good predictive capacity, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cem\u003e3.5 Validation of Logistic Regression model\u003c/em\u003eThe results of the logistic regression (RegLog) are shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The RegLog was carried out in order to assess whether the ternary blend samples could be classified into two groups: \u0026rsquo;Fraud\u0026rsquo;, corresponding to samples of goat milk suspected of being adulterated in some way, by adding water, cow milk or both in some proportion. Samples with a percentage of goat milk greater than 9 % would be considered \u0026rsquo;SNSF\u0026rsquo; (sample not suspected of fraud) by RegLog. Adulteration values of less than 1 % for goat milk were not evaluated, as fraudsters generally prefer to adulterate milk with slightly higher percentages, possibly in order to increase profits. Ali Ahmad (2009) reports 35. % added water and starch in raw milk.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eConfusion matrix used to evaluate the classification performance of Logistic Regression\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" morerows=\"2\" nameend=\"c2\" namest=\"c1\" rowspan=\"3\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e \u003cp\u003ePredicted\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eTraining (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;60, \u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.999)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003eValidation (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;19, \u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.947)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSNSF\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFraud\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSNSF\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFraud\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eExperimental\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSNSF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFraud\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe confusion matrix in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows that for training data, RegLog was able to correctly classify the samples, with \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.999. For the validation data, RegLog was also able to make a good classification, although it made a mistake when evaluating a single sample (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.947). This table shows that there were fewer SNSF samples and this is due to two factors. Firstly, there were far fewer SNSF samples in the data files used for training and validation, justified by the ternary mixture design, in which the samples with the lowest percentage of goat milk adulteration are closer to one of the vertices of the triangle shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (a). The other factor is due to the fact that the samples are randomly selected by the RegLog algorithm, and an SNSF sample may or may not be drawn. In the different draws made when carrying out this analysis, it was observed that the result was basically the same, with none or a single sample incorrectly classified by the algorithm.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eFT-NIR spectroscopy, when coupled with multivariate analysis, proved to be an effective method for both detecting and quantifying goat milk adulteration by the addition of water and cow milk, over a wide range of percentage values. Logistic regression was able to detect adulterated goat milk, with \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.947 (n\u0026thinsp;=\u0026thinsp;19), while PLS regression models were able to quantify the percentage of goat milk adulteration with R2 greater than 0.99, both for the addition of water and cow milk. These findings support the potential application of PLS and logistic regression as rapid screening tools for detecting economic fraud in goat milk.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eP.G.S. Conceptualization, Methodology, Data Analysis, Writing \u0026ndash; original draft. C.M.L. Investigation, Writing - review \u0026amp; editing, Visualization. J.L.C. Investigation, Methodology, Visualization, Resources. C.R.P.S. Investigation, Writing - review \u0026amp; editing, Visualization. D.K.S. Investigation, Writing - review \u0026amp; editing, Visualization. V.C.A. Conceptualization, Writing - original draft, Visualization. M.J.V.B. Conceptualization, Writing - review \u0026amp; editing, Visualization. S.V. Conceptualization, Writing - original draft, Visualization. R.A.R. Project administration, Conceptualization, Funding acquisition, Methodology, Investigation, Data curation, Supervision, Writing - review \u0026amp; editing.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAdam, A. A. H. (2009). Milk adulteration by adding water and starch at Khartoum State. \u003cem\u003ePakistan Journal of Nutrition\u003c/em\u003e, 8(4), 439\u0026ndash;440.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBoukria, O., Boudalia, S., Bhat, Z. F., Hassoun, A., \u0026amp; A\u0026iuml;t-Kaddour, A. (2023). Evaluation of the adulteration of camel milk by non-camel milk using multispectral image, fluorescence and infrared spectroscopy. \u003cem\u003eSpectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy\u003c/em\u003e, 300, 122932.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBritz, T. J., \u0026amp; Robinson, R. K. 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Adolfo Lutz Institute, S\u0026atilde;o Paulo, Brazil.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"dairy-science-and-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Dairy Science and Management](https:/dairysciencemanagement.biomedcentral.com/)","snPcode":"44363","submissionUrl":"https://submission.springernature.com/new-submission/44363/3","title":"Dairy Science and Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Authenticity, Multivariate modeling, Mixture, PLS, Logistic Regression","lastPublishedDoi":"10.21203/rs.3.rs-6801468/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6801468/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eGoat milk is a nutrient-rich food and due to its higher commercial value, it is not uncommon for it to be adulterated by the addition of water and cow milk. In this work, ternary mixtures of goat milk, cow milk and water were analyzed by FT-NIR(S), PLS and Logistic Regression. Exploratory investigation showed three ranges of spectral values most strongly associated with separation between the mixtures analyzed, 10800 to 9800, 8800 to 7200 and 6400 to 5600 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. The PLS models showed good predictive capacity to quantify the percentages of water, goat milk and cow milk in the ternary mixtures over a wide range of values. Logistical Regression was also good at classifying samples into two adulteration groups. FT-NIR spectroscopy, together with multivariate techniques, proved to be very promising as an analytical methodology for the rapid identification of adulteration and economic fraud in goat milk.\u003c/p\u003e","manuscriptTitle":"Detection and Quantification of Goat Milk Adulteration Using FT-NIR Spectroscopy combined with Partial Least Squares and Logistic Regression","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-05 10:28:07","doi":"10.21203/rs.3.rs-6801468/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-06-30T08:49:35+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-19T21:08:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"197343073714522040892427368373307171143","date":"2025-06-10T19:26:38+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-10T06:06:38+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"306586480666479158126720968098092530584","date":"2025-06-09T16:51:35+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-06-09T10:16:48+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-06-03T00:24:17+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-06-03T00:22:57+00:00","index":"","fulltext":""},{"type":"submitted","content":"Dairy Science and Management","date":"2025-06-02T10:47:23+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"dairy-science-and-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Dairy Science and Management](https:/dairysciencemanagement.biomedcentral.com/)","snPcode":"44363","submissionUrl":"https://submission.springernature.com/new-submission/44363/3","title":"Dairy Science and Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"6946483c-26c8-4e46-86f2-18a389c45bb4","owner":[],"postedDate":"June 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-07-30T08:08:44+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-05 10:28:07","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6801468","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6801468","identity":"rs-6801468","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}