MINI REVIEW article

Front. Anal. Sci., 03 March 2023

Sec. Chemometrics

Volume 3 - 2023 | https://doi.org/10.3389/frans.2023.1118590

Miniaturized NIR spectroscopy and chemometrics: A smart combination to solve food authentication challenges

  • Department of Chemistry, Sharif University of Technology, Tehran, Iran

Abstract

Over the years, technology has allowed more accurate, more effective, and prompt food integrity assessments to assure the quality and authenticity of food material. Thanks to the development of portable and hand-held near infrared (NIR) as a rapid, reliable, non-destructive, and user-friendly instrument, on-site food analysis is provided with more feasibility. However, miniaturized NIR devices have some significant challenges due to the presence of varying noise resources which can lead to misinterpretation. In this context, chemometric methods with the capability of resolution, identification, classification, and calibration play a pivotal role in achieving precise and in-depth comprehension of the data. In the present mini-review, we will discuss miniaturized NIR instrumentation, some chemometric concepts, and introduce the most popular algorithm in food authentication problem. The main feature of this review is avoiding mathematical details as much as possible to make the material accessible to a broad audience but highlighting the key features of chemometric methods with some simple illustrative examples in the scope of food authenticity.

Introduction

Growing concerns about food quality and authenticity, as well as the complexity of food fraud problems, have substantially raised the need for appropriate analytical techniques to assess the authenticity of food materials (McVey et al., 2021). Over the last decades, near-infrared (NIR) instrumentation has advanced dramatically, resulting in their wide application in food industry. The introduction of miniaturized (portable and handheld) NIR instruments with very small size, commercial engines that a variety of companies can build into products, and low-cost devices selling directly to the public have made it possible for both expert and non-expert users to do fast, easy, reliable and on-site food analysis (Müller-Maatsch and van Ruth, 2021; ). In spite of their many advantages, miniaturized NIR instruments have several limitations that make direct interpretation of the spectrum challenging. In many cases, the generated response requires spectral processing as well as statistical data analysis in order to find the spectral differences that are most useful for sample differentiation. Chemometric and machine learning methods, which are a subset of artificial intelligence (AI) have been proposed for dealing with these problems and improving the low resolution of miniaturized NIR measurements (). A large part of the development and application of the miniaturized NIR instrument in the food industry owes to the ability of various chemometric tools to improve the generated signal and thus enhance the interpretation. Existing literature has investigated the application of miniaturized NIR spectroscopy in the food industries with the focus on device technologies and various food scopes (Teixeira Dos Santos et al., 2013; ; ; McVey et al., 2021; ), but the necessitates, important concepts, and the role of various chemometric methods have not been discussed.

The presented mini-review provides an overview of miniaturized NIR instrumentation and represents a simple explanation of chemometric concepts and methods that a user should know when using a portable NIR instrument in the food study.

Miniaturized NIR instrument

NIR spectroscopy collects data by observing overtones and combination transitions in the 12.500–4,000 cm–1 or 800–2,500 nm spectral region where molecular vibrational excitations occur. These transitions are substantially less probable to occur than fundamental ones (IR and Raman), which result in a lower absorption index of a sample in the NIR area. A high number of overlapping bands in NIR spectra causes the lineshape to become broader, resulting in a reduction in resolution and making direct interpretation of spectra more challenging. A miniaturized NIR instrument has the same main parts as any other device that uses optical absorption spectroscopy: A light source, a wavelength selector, and a detector.

One of the most prevalent miniaturized NIR light sources is a tungsten halogen bulb. Even though heat sources are low-cost and reliable, their thermal stability is a major concern for handheld NIR devices as they employ in-field analysis where temperatures vary widely. The easiest way suggested by vendors is performing regular reference scans to keep the latest background signal. The second common NIR radiation sources are light-emitting diodes (LEDs) which have specefic features make them very sutible for miniaturezed NIR design. They are very small, cheap, durable with low voltage and power required. Nevertheless, LEDs have some limitations in spectroscopy. The radiation band’s narrowness is one of these limitation. For example, a gallium arsenide (GaAs) LED has a peak emission of 870 nm and a bandwidth of just 50 nm. In addition, there is still a severe lack of available LEDs in NIR region.

Miniaturized NIRs wavelength selector are varies in compared to benchtop ones, which is more besed on Michelson interferometer. Using micro electromechanical systems (MEMS), it would be possible to miniaturize a number of wavelength selectors; or micro-opto-electromechanical systems (MOEMS) if micro-optics is also included. Generally, they can be based on the more suitable and feasible machanism such as the Fabry–Perot interferometer, Hadamard mask, linear variable filter (LVF), or digital micromirror array.

Regarding to the miniaturized NIR detector, photovoltaic Si diodes present an appropriate level of sensitivity within the range of 14,285–9,100 cm-1 (700–1,100 nm), and so, ideal only for more miniature, low-cost spectrometers. On the other hand, the S/N ratio achieved by this approach is poor and needs some cut-off filter to decrease the sensitivity of the detector to sunlight. In the range of 9,500–400 cm-1 (1,050–2,500 nm), InGaAs photodetectors perform well and are the most commonly used detectors which allows for fast scanning with high signal-to-noise ratios. InGaAs detectors are faster in response and have high quantum performance along with the low dark current for a given sensor surface, allowing for fast scanning with high signal-to-noise ratios.

Another important feature in miniaturized NIR is optical material. To a vast extent, optical materials which do not absorb light in the visible range are also transparent over a significant region of the infrared light spectrum. Notably, this means that glass optics may be employed for; however, for optimal performance in the long-wave (LW-NIR) range, high-quality fused silica (also known as fused quartz) optic material may be needed. Because there are no of alkali halides in fused quartz, the cost of miniaturized NIRs is reduced, their operability in humid conditions is enhanced, and their performance for on-site and monitoring analysis is highly improved. When operating in contact mode and rugged analysis, it is preferable to have a scratch-resistant optical window at the sample interface for reliable functioning. This function is often performed by sapphire, although owning to high refractive index of sapphire, they undergo some optical loss and can only have a proper function in multi-channel spectrometers (; ; ; ; ).

Why we should use chemometrics?

Modern miniaturized NIR instruments provide multivariate information describing the composition, state, or evolution of a specific chemical process. However, NIR instruments have significant challenges due to various issues in their spectroscopic data. On the other hand, a portable NIR spectrometer compared to its laboratory counterpart that is strictly evaluated based on conventional laboratory parameters for analytical performance, would typically perform less effectively in terms of resolution, signal throughput, and signal-to-noise ratio (SNR). Moreover, fixed or predetermined spectral range and resolution of portable NIR instruments as well as the fit-for-purpose operational requirements, such as deployment potential must also be considered. Besides the complex nature of the data structure, portable systems may provide answers requiring complex data interpretation or assessment on the part of the operator. Thus, data pretreatment and chemometric tools are required for qualitative and quantitative analysis with the aim of improving signal quality, enhancing SNR, solving peak shifting/overlapping problems, and handling imperfect and variable input data. Herein, some of the basic chemometric tools for the analysis of NIR data will be discussed.

Preprocessing

The NIR data preprocessing step has evolved into an integral part of chemometric modeling. The primary objective of preprocessing is to eliminate artifacts of spectra to enhance capability of exploration, calibration, and classification. The source of variation depends on various factors in a NIR measurement in both reflectance and transmittance modes. For instance, in solid food samples with different particle sizes or heterogeneous shape, the main reasons for data variation that may lead to shifts in the baseline are differences in effective route length and dispersion of the light source (scattering). For liquid samples like oil, scattering is dependent not only on the path but also on the liquid concentration. The commonly utilized pre-processing approaches in NIR spectral data can be categorized into two groups: Scatter correction techniques and spectral derivatives.

The scatter-correction preprocessing techniques consists of multiplicative scatter correction (MSC), inverse MSC (IMSC), extended MSC (EMSC), extended inverse MSC (EIMSC), de-trending, standard normal variate (SNV) and normalization. These methods are implemented with the goal of decreasing the physical scatter variability.

Norris-Williams (NW) derivatives and Savitzky-Golay (SG) polynomial derivative filters are categorized in the spectral derivatives methods. The aim of this appraoch is to eliminate or reduce the effect of both additive and multiplicative effects in the spectra. Both strategies include a spectrum smoothing step before computing the derivative (1st order, 2nd order, … ) to reduce the negative effect on the signal-to-noise ratio that would occur with a conventional finite difference derivative (Rinnan et al., 2009; Mishra et al., 2020; Schoot et al., 2020).

Pattern recognition

Regarding food authentication, it is crucial to determine whether the sample/object meets the expected criteria (standards) or belongs to the interest group or class. Simply put, we usually seek to categorize samples based on their individual and distinct features or, more particularly, classifying them. From the perspective of chemometrics, this notion is included in pattern recognition methods which are defined as a primarily classification to assign samples into classes or groups. Classification methods can be categorized in a variety of ways based on which of their features is of most concern. As one of the main attributes, classification methods can be divided into supervised and unsupervised approaches. Supervised methods try to classify objects based on their features by using a training set, which consists of samples that are assigned to predetermined classes. In unsupervised methods, there are no labeled (predefined) classes and samples are distributed in different parts of the dataspace based on the similarity and dissimilarity among the variables. Generally, in a supervised technique, as opposed to an unsupervised one, there is typically some prior knowledge about the sample and its characteristics (; ).

Unsupervised data exploration methods as the first step of data analysis

Data exploration methods assist in extracting buried information from the data and visualizing it in a manner that is simple to comprehend and interpret. One of the most popular and widely-used exploration methods is the principal component analysis (PCA), which analyzes data regarding all variables (multivariate approach). PCA is a bilinear decomposition/projection method that reduces data dimensions to a small number of factors known as principal components (PCs) or latent variables (LVs), which are linear combinations of original variables. In addition, there are non-linear exploratory methods such as self-organizing maps (SOMs), Kohonen networks, projection pursuit and curvilinear component analysis (CCA) that are not yet widely used in the food industry, whose potential can be investigated in future studies.

Clustering techniques are the other well-known exploratory multivariate data analysis. The prime objective of cluster analysis is discovering groups in a data set. This is achieved by using the concept that objects with more similarity and less distance in the variable space form a cluster. A popular and widely-used technique in clustering is hierarchical clustering analysis (HCA) which operates based on the calculation of different distances among samples like Euclidean, Mahalanobis, and Manhattan distance. In HCA, two samples with the most similarity are identified and joined in a cluster. The similarity index of the new cluster in comparison to all other objects is computed based on the employed method (Vigni et al., 2013).

Class modeling vs discrimination approach

The other classification characteristic is defined using the terms discrimination and class modeling. Class modeling and discrimination methods are two types of supervised classification techniques. Despite the fact that both methods have the same aim, there are major differences in the implications of their usage.

In the discrimination strategy, the classification model is built based on the differences among samples/objects from various classes, resulting in hypersurfaces (multidimensional surfaces) that divide the whole variable space into the number of classes. Therefore, each individual (prediction) sample belongs to one of the model classes, regardless of whether it relates to them. Supplementary Figure S1A illustrates a discrimination analysis in which the entire space is comprised of two sub space according to two classes (solid circles and stars). As is evident from prediction samples (hollow shapes), triangle and square objects that are irrelevant to primary classes are classified as one of them.

Class modeling approaches, on the other hand, concentrate on the similarities among samples belonging to the same category (target class) instead of the differences among classes. By taking this approach, each class is modeled independently and positioned in its own isolated area in the feature space of the model (red dashed and dots in Supplementary Figure S1B). Supplementary Figure S1B shows that there are three possible outcomes for a prediction sample: i) Belonging to one of the two classes represented by the hollow circle and star, ii) belonging to both classes represented by the hollow square, or iii) neither class (hollow triangle).

In summary, the discriminating models always classify a new object into one of the predefined classes, while in the class modeling, a new object can belong to predefined classes or not. Therefore, to avoid misunderstandings, users should be attentive when using discrimination strategies. Discrimination techniques are often used when the number of classes is small and there is the guarantee that the tested samples exclusively belong to the predefined classes. As a result, it can be concluded that class modeling approaches are preferable for addressing food authentication (Rantalainen et al., 2007; Pomerantsev, 2018; Małyjurek et al., 2020).

Linear and non-linear classification

Another differentiation factor between the classification strategies is based on the mathematical form of the functional relationship, referring to the geometric shape used to separate variables in multidimensional (feature) space. Within this frame, the main categorization is between linear and non-linear approaches, which in the case of non-linearity, there are some subdivisions like quadratic and polynomial. When using linear approaches, decision boundaries are represented as linear functions of the initial variables. This decision boundary can be a line, a plane, or a hyperplane to separate, respectively, two, three, or more than three dimensions. On the contrary, in the non-linear approach, a more complicated hypersurface is responsible for splitting data space according to existing classes. For example, in the quadratic approach, the decision boundaries can be hyperellipsoids, hyperparaboloids or hyperspheres (Supplementary Figure S2) (; ; Rocha et al., 2020).

Multivariate calibration

Calibration techniques provide quantitative information by establishing a relationship between instrumental measurements to analytes of interest. In the basic case, calibration model represents a relationship between a single response or predictor of a device, such as a single wavelength absorbance in spectroscopy, to a concentration of an object/sample which is called univariate calibration. However, currently, the employed approaches are multivariate calibrations in which multiple measurements are taken rather than just one (i.e., multiple wavelengths or spectrum of samples); consequently, for a single measurement, a vector generates. In the both univariate and multivariate calibration, there are two main roles and steps i) calibration for model construction and ii) prediction of new samples. In general, calibration methods can be divided into linear and non-linear models. Examples of more frequently used linear models are multiple linear regression (MLR), principal component regression (PCR), partial least squares (PLS) and multivariate curve resolution-alternating least squares (MCR-ALS). In other words, non-linear models include a vast range of machine learning techniques like as support vector machine (SVM), artificial neural network (ANN) (Westad et al., 2013; Saeys et al., 2019). Figure 1A shows a general view of the classification of chemometric methods.

FIGURE 1

Model validation

The development of a model is not complete without validation of its performance. Model validation is crucial in the context of food authentication in order to prevent misinterpretation of classification, and quantification of unknown/prediction sample. The best way to evaluate the validity of a model is by using representative independent test samples. In the case where the number of samples is sufficient, the data set is usually divided into a ratio of 70% training and 30% testing. On the other hand, cross-validation methods are used for internal validation of the developed models. Depending on the type of data and the algorithm used, one/a group of data set is excluded and the model is built with the remaining samples. Then the excluded samples are evaluated in the developed model and the prediction residuals are calculated. This cycle continues until the evaluation of all samples and finally using the prediction residuals, validation residual variance and root mean square error in prediction (RMSEP) are computed (Westad et al., 2013; Westad and Marini, 2015).

Application of miniaturized NIR spectroscopy and chemometrics in food industry

The practical application of state-of-the-art miniaturized NIR spectroscopy has provided solutions to various food industry challenges (i.e., quality, authenticity, traceability etc.,). On-site checking of food quality, monitoring products at various stages of production, and assessing food ingredients without opening food packaging are among the significant benefits of miniaturized NIR. The low resolution of these instruments, however, necessitates that they be coupled with data analysis tools such as chemometrics. Figure 1B shows the steps of chemometric data analysis methods that are commonly applied to NIR spectra. In addition, the pie chart in Figure 1C represents a scheme of the frequency of chemometric methods used in food studies regard to miniaturized NIR instruments. As it is evident, PCA in exploration, PLS-DA in classification, and PLSR in calibration are the most widely-used chemometric techniques. Another noteworthy fact is that SIMCA has been only used in a few studies, although it is a high-potential method in the context of food authenticity. Various studies have investigated the capability of miniaturized NIR in the field of food authentication (; Müller-Maatsch and van Ruth, 2021; ). However, the application of miniaturized NIR is increasing considerably. Table 1 shows some of the applications of miniaturized NIR coupled with chemometrics for food analysis. One research compares a portable NIR device to a benchtop FT-NIR spectrometer for identifying Atlantic cod fillets and patties from haddock. LDA and SIMCA, pre-treating spectral data with various techniques and model validation both internally and externally, was employed. Best LDA models predicted 100% correctly. Best SIMCA models predicted with sensitivity >65% and specificity >74%. McNemar test indicated no significant differences (p > 0.05) across the instruments (). Three portable NIR devices were used to test almond flour authenticity with a benchtop FT-NIR. 54 almond flours were contaminated with cheap flours in Brazil. SIMCA, DD-SIMCA, and OCPLS for classification and PLSR used for predicting sample purity. Classification findings obtained 100% sensitivity and more than 95% specificity for samples with adulterant amounts over 5% (w/w). PLS models revealed R2 values over 0.90 and RMSEP between 3.2% and 4.8% for purity. According to multivariate models, portable NIR equipment can identify and quantify contaminated almond flour (Marcelino et al., 2023). Portable NIR spectroscopy coupled with multivariate supervised classification was suggested to identify peanuts, Brazil nuts, macadamia nuts, and pecan nuts in cashew nut samples, covering a broad concentration range (10%–0.1% w/w). Algorithms were established to estimate cashews pure and adulterated with peanuts, Brazil nuts, macadamia nuts, and pecan nuts. Interval partial-least-squares regression (iPLS), genetic algorithm (GA), and iPLS-GA were explored as variable selection procedures. PLS-DA paired with iPLS-GA offered the best results, with sensitivity between 81% and 93% and selectivity between 94% and 100%. (Sheng et al., 2022). We will summarized some of previous studies based on the variety of chemometrics method and according to ().

TABLE 1

ScopeTargetMiniaturized NIRChemometric methodGeneral resultRef
DairyAuthentication of organic milkMicroNIR 1700PCA, PLS-DAAcceptable discrimination between organic and conventional milk; less-successful class assignment of pasture milk samples
Calssification milk sample based on their quality for improved monitoring in dairy facilitiesmicroPHAZIRPLSR, ANNGood performance in real-time monitoring of each cow sampleMuñiz et al. (2020)
Determination of main component in milkFieldSpec Pro FR (ASD Inc.)LS-SVM, PLSRHandheld SW-NIR spectrometer was determined to be an excellent detector for the milk powder analysis, suiting the needs of industrial applicationWu et al. (2008)
Quantitative analysis of the irradiation dose (0–6.0 kGy) in milk powder; irradiation by60Co γ-raysFieldSpec (ASD Inc.)RC, PLSR, LS-SVMProviding fast and on-site detection of irradiation doses of milk powder in a food-safety-monitoring scenario
Meat and fishAuthentication of chicken meat by miniaturized NIR spectrometerMicroNIR 1700PLS-DA, CP-ANN, SVM, RSDERapid and low-cost authentication and quality control of meat with miniaturized NIRParastar et al. (2020)
Miniaturized NIR spectroscopy as an onsite model for studying pork microbiologymicroPHAZIRPCA, PLSR, MPLSMiniaturized NIR spectroscopy can accurately predict pork’s microbiological state onsite; packing environment has no effectPrado and Fernández-ibáñez (2011)
Classifying chicken parts (breasts, thighs, drumsticks) using a portable NIR spectrometer; analyzing physical and chemical properties (pH, color) and chemical composition (protein, fat, moisture, and ash)DLN NIRscan NanoLDA, RF, SVMPortable NIR spectroscopy accurately classified chicken meat in the processing line and authenticated shelf samples of processed itemsMarivel et al. (2018)
Investigating whole fish and fillets using a miniaturized NIR spectrometer; separating high-quality from low-quality fishMicroNIR 1700PCA, SIMCASIMCA analysis of the spectra measured by MicroNIR on the skin or flesh of whole fish or fish fillets provided correct authentication of the fish sample Fish
Estimate nutrient content (protein, lipids, and moisture) and distinguish between sources (farmed vs wild fish) and conditions (fresh or defrosted fish)Tellspec Enterprise SensorPCA, LDA, PLSR, RF, LR, SVM, XGBTellspec sensor performed well in predicting nutritional values (protein, lipids, and moisture) and authenticating the source and condition of all investigated fish species
Fruits and VegetablesDeveloping a portable NIR spectrometer to distinguish between organic and inorganic pineapple fruits; predicting total soluble solid. FeasibilitySCiOKNN, PCA, LDA, PLSR, MSC-PCA-LDAPortable NIR spectrometer with chemometric instruments proved suited for quick non-destructive analysis of pineapple quality; effective identification of pineapple fraud-mislabeling conventionally produced fruits as organic ones
Feasibility study for using a miniaturized and benchtop NIR instrument to predict quality-related parameters (soluble solid content, firmness, variety and postharvest storage duration under refrigeration) in intact plumsmicroPHAZIR, Perten DA-7000MPLS, PLSR, PCRSimilar levels of accuracy for miniature and benchtop NIR for the measurements of soluble solid content, variety, and refrigerated-storage time; the prediction model constructed using the diode-array spectrometer yielded superior results for the prediction of firmnessPérez-marín et al. (2010)
Beverage and syrupInvestigation of the capability of miniaturized NIR spectroscopy for assessment of the quality index of matcha teaNIRscan NanoPLSR, Si-PLS, GA-PLS, CARS-PLS, RF-PLSA model with good ability for predicting and classifying the content of polyphenols and amino acids in matcha tea was developedWang et al. (2019)
Feasibility study on determination of sugar (sucrose) contents in everyday drinks using miniaturized NIR spectroscopyNIRScan NanoOLS, SLR, MLR, SVM, RF, MPLHigh-quality model performance for sucrose content analysis

Some of the applications of miniaturized NIR coupled with chemometrics for food analysis.

PLSR, partial least square regression, PCA, principal component analysis, PLS-DA, partial least squares discriminant analysis, MPLS, modified partial least squares, SVM, support vector machine, LDA, linear discriminant analysis, SVR, support vector regression, SIMCA, soft independent modeling of class analogy, KNN, k-nearest neighbors, MLR, multiple linear regression, RF, random forests-, ANN, artificial neural network, CARS, competitive adaptive reweighted sampling, OPLS-DA, orthogonal projections to latent structures discriminant analysis, LS-SVM, least-squares support vector machine, OLS, ordinary least squares, SLR, single linear regression, MPL, multilayer perceptron, XGB, extreme gradient boosting, RSDE, random subspace discriminant ensemble, CP-ANN, counter-propagation artificial neural network.

Conclusion

The dramatic advancement of miniaturized NIR spectrometers (i.e., handheld and portable) has revolutionized rapid, facile, on-site and non-destructive analysis of samples in food chemistry. However, these instruments have significant challenges due to various issues in their spectroscopic data, like baseline contribution, noise, lack of repeatability, peak overlap, and low resolution. In this context, chemometric/machnine learning techniques attempt to extract the required information from spectra and explore this spectral information for qualitative or quantitative purposes through mathematical resolution, pattern recognition, and calibration.

We believe this mini-review article is of general interest to the whole food chemistry community as everybody hears these buzzwords daily, but the real ideas and potential behind the miniaturized spectroscopy and chemometrics are not widely known and understood yet. We hope this review will promote further research on miniaturized spectroscopy in food to solve different problems.

Statements

Author contributions

AA: Formal analysis, investigation, methodology, writing—original draft. HP: Concenptualization, Funding and Writing-editing.

Funding

The current work was performed as a part of grant no. G960613.

Acknowledgments

The authors would like to thank Sharif University of Technology for support of this project.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/frans.2023.1118590/full#supplementary-material

Abbreviations

ANN, artificial neural network; CARS, competitive adaptive reweighted sampling; KNN, k-nearest neighbors; LDA, linear discriminant analysis; MLR, multiple linear regression; MPLS, modified partial least squares; OPLS-DA, orthogonal projections to latent structures discriminant analysis; PCA, principal component analysis; PLS-DA, partial least squares discriminant analysis,; PLSR, partial least square regression; RF, random forests; SIMCA, soft independent modeling of class analogy; SVM, support vector machine; SVR, support vector regression.

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Summary

Keywords

chemometrics, miniaturized NIR spectroscopy, food authentication, classification, calibration

Citation

Amirvaresi A and Parastar H (2023) Miniaturized NIR spectroscopy and chemometrics: A smart combination to solve food authentication challenges. Front. Anal. Sci. 3:1118590. doi: 10.3389/frans.2023.1118590

Received

07 December 2022

Accepted

13 February 2023

Published

03 March 2023

Volume

3 - 2023

Edited by

Stefano Fornasaro, University of Trieste, Italy

Reviewed by

Mohammed Kamruzzaman, University of Illinois at Urbana-Champaign, United States

Updates

Copyright

*Correspondence: Hadi Parastar,

This article was submitted to Chemometrics, a section of the journal Frontiers in Analytical Science

Disclaimer

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

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