Local Modeling by Adapting Source Calibration Models to Analyte Shifted Target Domain Samples Without Reference Values.

Spectral multivariate calibration aims to derive models characterizing mathematical relationships between sample analyte amounts and corresponding spectral responses. These models are effective at predicting target domain sample analyte amounts when target samples are within the analyte and spectral calibration source domain. Models fail when target samples shift (analyte amounts and/or spectra) from the original calibration domain model. A total recalibration solution requires acquisition of new sample reference values and spectra. However, obtaining enough reference values to distinguish the target domain may be challenging or expensive. A simpler approach adapts the original model to the target domain using target sample spectra without analyte reference values (unlabeled). Analytical chemists have developed several machine learning algorithms using unlabeled regression domain adaptation processes. Unfortunately, prediction accuracy declines for these methods depending on how much the target domain analyte distribution has shifted from the calibration distribution, and regression transfer learning methods are instead needed. Regression domain adaptation and transfer learning are often referred to as model updating in analytical chemistry, but regression domain adaptation only applies to spectral shifts. The regression transfer learning method presented in this paper named null augmentation regression constant analyte (NARCA) leverages unlabeled repeat spectra of a single target sample to update an original calibration model to the shifted target domain sample. With sample repeat spectra, the analyte amount can be assumed constant or nearly constant for NARCA and because models are formed for one sample, NARCA operates as a local modeling method. The performance of NARCA as a regression transfer learning method is evaluated using five near-infrared data sets.

Physicochemical Responsive Integrated Similarity Measure (PRISM) for a Comprehensive Quantitative Perspective of Sample Similarity Dynamically Assessed with NIR Spectra.

Determining sample similarity underlies many foundational principles in analytical chemistry. For example, calibration models are unsuitable to predict outliers. Calibration transfer methods assume a moderate degree of sample and measurement dissimilarities between a calibration set and target prediction samples. Classification approaches link target sample similarities to groups of similar class samples. Although similarity is ubiquitous in analytical chemistry and everyday life, quantifying sample similarity is without a straightforward solution, especially when target domain samples are unlabeled and the only known features are measurable, such as spectra (the focus of this paper). The process proposed to assess sample similarity integrates spectral similarity information with contextual considerations among source analyte contents, model, and analyte predictions. This hybrid approach named the physicochemical responsive integrated similarity measure (PRISM) amplifies hidden-but-essential physicochemical properties encoded within respective spectra. PRISM is tested on four near-infrared (NIR) data sets for four diverse application areas to show efficacy. These applications are the assessment of prediction reliability and model updating for model generalizability, outlier detection, and basic matrix matching evaluation. Discussion is provided on adapting PRISM to classification problems. Results indicate that PRISM collects large amounts of similarity information and effectively integrates it to produce a quantitative similarity evaluation between the target sample and a source domain. The approach is also useful for biological samples with additional physiochemical variations. While PRISM is dynamically tested on NIR data, parts of PRISM were previously applied to other data types, and PRISM should be applicable to other measurement systems perturbed by matrix effects.

Calibration Model Updating to Novel Sample and Measurement Conditions without Reference Values.

Updating a calibration model formed in original (primary) sample and spectral measurement conditions to predict analyte values in novel (secondary) conditions is an essential activity in analytical chemistry in order to avoid a complete recalibration. Established model updating methods require sample analyte reference values for a small set of secondary domain samples (labeled data) to be used in updating processes. Because obtaining reference values is time consuming and is the costly part of any calibration, methods are needed that do not require labeled secondary samples, thereby allowing on demand model updating. This paper compares model updating methods with and without labeled secondary samples. A hybrid model updating approach is also developed and evaluated. Unfortunately, a major impediment to adapting a model without secondary analyte reference values has been model selection. Because multiple tuning parameters are commonly involved in model updating methods, thousands of models are formed, making model selection complex. A recently developed framework is evaluated for automatic model selection of several two to three tuning parameter-based model updating methods without secondary analyte reference values (labels). The model selection method is based on model diversity and prediction similarity (MDPS) of the unlabeled samples to be predicted. The new secondary samples to be predicted can be used to form the updated models and again to select the final predicting models. Because models are formed and selected on demand to directly predict target samples, complicated cross-validation processes are not needed. Four near-infrared data sets covering 40 model updating situations are evaluated showing that MDPS can select reliable updated models outperforming or rivaling prediction errors from total recalibrations with secondary reference values.

Reliable Model Selection without Reference Values by Utilizing Model Diversity with Prediction Similarity.

Predictive modeling (calibration or training) with various data formats, such as near-infrared (NIR) spectra and quantitative structure-activity relationship (QSAR) data, provides essential information if a proper model is selected. Similarly, with a general model selection approach, spectral model maintenance (updating) from original modeling conditions to new conditions can be performed for dynamic modeling. Fundamental modeling (partial least-squares (PLS) and others) and maintenance processes (domain adaptation or transfer learning and others) require selection of tuning parameter(s) values to isolate models that can accurately predict new samples or molecules, e.g., number of PLS latent variables to predict analyte concentration. Regardless of the modeling task, model selection is complex and without a reliable protocol. Tuning parameter selection typically depends on only one model quality measure assessing model bias using prediction accuracy. Developed in this paper is a generic model selection process using concepts from consensus modeling and QSAR activity landscapes. It is a consensus filtering approach that prioritizes model diversity (MD) while conserving prediction similarity (PS) fused with a common bias-variance trade-off measure. A significant feature of MDPS is that a cross-validation scheme is not needed because models are selected relative to predicting new samples or molecules, i.e., model selection uses unlabeled samples (without reference values) for active predictions. The versatility and reliability of MDPS model selection is shown using four NIR data sets and a QSAR data set. The study also substantiates the Rashomon effect where there is not one best model tuning parameter value that provides accurate predictions.

Ultrasonic-assisted catalytic transfer hydrogenation for upgrading pyrolysis-oil.

Recent interest in biomass-based fuel blendstocks and chemical compounds has stimulated research efforts on conversion and upgrading pathways, which are considered as critical commercialization drivers. Existing pre-/post-conversion pathways are energy intense (e.g., pyrolysis and hydrogenation) and economically unsustainable, thus, more efficient process solutions can result in supporting the renewable fuels and green chemicals industry. This study proposes a process, including biomass conversion and bio-oil upgrading, using mixed fast and slow pyrolysis conversion pathway, as well as sono-catalytic transfer hydrogenation (SCTH) treatment process. The proposed SCTH treatment employs ammonium formate as a hydrogen transfer additive and palladium supported on carbon as the catalyst. Utilizing SCTH, bio-oil molecular bonds were broken and restructured via the phenomena of cavitation, rarefaction, and hydrogenation, with the resulting product composition, investigated using ultimate analysis and spectroscopy. Additionally, an in-line characterization approach is proposed, using near-infrared spectroscopy, calibrated by multivariate analysis and modeling. The results indicate the potentiality of ultrasonic cavitation, catalytic transfer hydrogenation, and SCTH for incorporating hydrogen into the organic phase of bio-oil. It is concluded that the integration of pyrolysis with SCTH can improve bio-oil for enabling the production of fuel blendstocks and chemical compounds from lignocellulosic biomass.

Application of a Hybrid Fusion Classification Process for Identification of Microplastics Based on Fourier Transform Infrared Spectroscopy.

Microplastic research is an emerging field. Consistent accurate identification of microplastic polymer composition is vital for understanding the effect of microplastic pollution in the environment. Fourier transform infrared (FT-IR) spectroscopy is becoming commonplace for identifying microplastics. Conventional spectral identification is based on library searching, a process that utilizes a search algorithm against digital databases containing single spectra of pristine reference plastics. Several conditions on environmental microplastic particles such as weathering, additives, and residues cause spectral alterations relative to pristine reference library spectra. Thus, library searching is vulnerable to misidentification of microplastic samples. While a classification process (classifier) based on a collection of spectra can alleviate misidentification problems, optimization of each classifier (tuning parameter) is required. Additionally, erratic results relative to the particular optimized tuning parameter can occur when microplastic samples originate from new environmental or biological conditions than those defining the class. Presented in this study is a process that utilizes spectroscopic measurements in a hybrid fusion algorithm that depending on the user preference, simultaneously combines high-level fusion with low- and mid-level fusion based on an ensemble of non-optimized classifiers to assign microplastic samples into specific plastic categories (classes). The approach is demonstrated with 17 classifiers using FT-IR for binary classification of polyethylene terephthalate (PET) and high-density polyethylene (HDPE) microplastic samples from environmental sources. Other microplastic types are evaluated for non-class PET and HDPE membership. Results show that high accuracy, sensitivity, and specificity are obtained thereby reducing the risk of misidentifying microplastics.

Self-Optimized One-Class Classification Using Sum of Ranking Differences Combined with a Receiver Operator Characteristic Curve.

A significant and common problem in analytical chemistry is determining if a sample belongs to a specific class, e.g., establishing if a food product is genuine or counterfeit or a tissue sample is benign or malignant. This problem is termed one-class classification (class modeling). Problematic with class modeling is determining which one-class classifier to use followed by the challenge of optimizing the chosen classifier (identifying the best tuning parameter value(s)). With spectroscopic data, two other conundrums arise: which data preprocessing method(s) and spectral region(s) to use. Presented in this paper is a hybrid fusion process that can combine nonoptimized classifiers across multiple instruments, preprocessing methods, and measurements. Instead of optimizing classifiers, a window of tuning parameters is used for each classifier. The flexible fusion method of sum of ranking differences (SRD) is applied to combine all assessment values. Defining the best SRD ranking value (threshold) for determining class membership is the one tuning parameter value needed. However, this SRD ranking value is automatically optimized by using a receiver operator characteristic (ROC) curve. The approach is demonstrated on two analytical data sets. The first is a beer authentication sample set measured on five instruments: near-infrared, mid infrared (MIR), ultraviolet, visible, and thermogravimetric. Three different fusion protocols of all five instruments are demonstrated. The second data set is MIR spectra of strawberry puree with two categories: strawberry puree and nonstrawberry puree. Fusing nonoptimized classifiers provides reliable classifications relative to accuracy, sensitivity, and specificity.

Identifying Chemical, Physical, and Instrumental Matrix Matched Samples by Leveraging Spectral Model Regression Vectors.

Developing spectroscopic calibration models requires calibration samples that mimic as much as possible new sample compositions as well as measurement conditions. This requirement is known as matrix matching calibration samples to new samples, that is, samples are matrix matched chemically, physically, and instrumentally. To accomplish this task, calibration sets have large sample numbers to span the expected sample matrix variations. This large range of calibration variability can result in poor performance. Preferred is a calibration set distinctly matched to the new samples. However, assessing whether each sample in a particular calibration set is appropriately matched to new samples relative to the specific analyte content and all other constituents is not an easy task. It is well documented that even though calibration samples are spectral matches to new sample spectra (have similar measured spectra), the calibration set is usually not fully matrix matched to new sample compositions. For example, using a spectral similarity measure such as Euclidean distance, the same calibration samples are deemed spectral matches to new samples regardless of the analyte of interest. This work presents a process to assess underlying sample matrix interactions between calibration model regression vectors and new sample spectra allowing fully matrix matched samples to be identified. The process is general and applicable to other situations such as matching historical batch processing data where references values are not known for new samples (unlabeled). Two data sets are used to demonstrate the functionality of the process. One consists of nuclear magnetic resonance spectra for mixtures of three alcohols and the other is near-infrared corn spectra with four prediction properties measured on three instruments. General trends are reported for a few of the possible data situations. Calibration samples identified as matrix matched to new samples are shown to predict the new samples with the lowest prediction errors.

Consensus Classification Using Non-Optimized Classifiers.

Classifying samples into categories is a common problem in analytical chemistry and other fields. Classification is usually based on only one method, but numerous classifiers are available with some being complex, such as neural networks, and others are simple, such as k nearest neighbors. Regardless, most classification schemes require optimization of one or more tuning parameters for best classification accuracy, sensitivity, and specificity. A process not requiring exact selection of tuning parameter values would be useful. To improve classification, several ensemble approaches have been used in past work to combine classification results from multiple optimized single classifiers. The collection of classifications for a particular sample are then combined by a fusion process such as majority vote to form the final classification. Presented in this Article is a method to classify a sample by combining multiple classification methods without specifically classifying the sample by each method, that is, the classification methods are not optimized. The approach is demonstrated on three analytical data sets. The first is a beer authentication set with samples measured on five instruments, allowing fusion of multiple instruments by three ways. The second data set is composed of textile samples from three classes based on Raman spectra. This data set is used to demonstrate the ability to classify simultaneously with different data preprocessing strategies, thereby reducing the need to determine the ideal preprocessing method, a common prerequisite for accurate classification. The third data set contains three wine cultivars for three classes measured at 13 unique chemical and physical variables. In all cases, fusion of nonoptimized classifiers improves classification. Also presented are atypical uses of Procrustes analysis and extended inverted signal correction (EISC) for distinguishing sample similarities to respective classes.

Feasibility Assessment of Synchronous Fluorescence Spectral Fusion by Application to Argan Oil for Adulteration Analysis.

Synchronous fluorescence spectroscopy (SFS) is used for quantitative analysis as well as for qualitative analysis, such as with classification methods. With SFS, determination of a useful wavelength interval between the excitation and emission wavelengths (Δλ) is required. There are a multitude of Δλ intervals that can be evaluated and optimization of the best one is complex. Presented here is a fusion approach for combining Δλ intervals, thereby negating the need to perform the selection by a skilled operator. To demonstrate the feasibility of omitting selection of the best Δλ interval, adulterated argan oil samples are studied. Argan oil is made from the argan tree, endemic to southwestern Morocco, and is well-known for its cosmetic, pharmaceutical, and nutritional applications. It is considered a luxury product and exported from Morocco around the world. Consequently, detection of argan oil adulteration followed by quantitative analysis of the adulterant concentration is important. This study uses fusion of SFS spectra obtained at ten Δλ intervals to first detect adulteration of argan oil by corn oil and then determination of the corn oil content. For detection of adulteration, 15 one-class classification methods were used simultaneously over the ten Δλ sets of SFS spectra. For tuning parameter dependent classifiers such as Mahalanobis distance, non-optimized classifiers are used. Raw classification values are used, removing the need to set classifier-dependent threshold values, albeit, ultimately, a fusion decision rule is needed for classification. For quantitative analysis, two calibration approaches are evaluated with fusion of these ten Δλ SFS spectral data sets. One is multivariate calibration by partial least squares (PLS). The second approach is a univariate calibration process where the SFS spectra are summed over respective SFS spectral ranges, also known as the area under the curve (AUC). For adulteration detection and quantitation of the corn oil, prediction errors decrease with fusion compared to individually using the ten Δλ interval SFS specific data sets. For this argan oil data set, the AUC method generally provides equivalent prediction errors to PLS.

Consensus Outlier Detection Using Sum of Ranking Differences of Common and New Outlier Measures Without Tuning Parameter Selections.

Sample outlier detection is imperative before calculating a multivariate calibration model. Outliers, especially in high-dimensional space, can be difficult to detect. The outlier measures Hotelling's t-squared, Q-residuals, and Studentized residuals are standard in analytical chemistry with spectroscopic data. However, these and other merits are tuning parameter dependent and sensitive to the outlier themselves, i.e., the measures are susceptible to swamping and masking. Additionally, different samples are also often flagged as outliers depending on the outlier measure used. Sum of ranking differences (SRD) is a new generic fusion tool that can simultaneously evaluate multiple outlier measures across windows of tuning parameter values thereby simplifying outlier detection and providing improved detection. Presented in this paper is SRD to detect multiple outliers despite the effects of masking and swamping. Both spectral (x-outlier) and analyte (y-outlier) outliers can be detected separately or in tandem with SRD using respective merits. Unique to SRD are fusion verification processes to confirm samples flagged as outliers. The SRD process also allows for sample masking checks. Presented, and used by SRD, are several new outlier detection measures. These measures include atypical uses of Procrustes analysis and extended inverted signal correction (EISC). The methodologies are demonstrated on two near-infrared (NIR) data sets.

Fusion strategies for selecting multiple tuning parameters for multivariate calibration and other penalty based processes: A model updating application for pharmaceutical analysis.

New multivariate calibration methods and other processes are being developed that require selection of multiple tuning parameter (penalty) values to form the final model. With one or more tuning parameters, using only one measure of model quality to select final tuning parameter values is not sufficient. Optimization of several model quality measures is challenging. Thus, three fusion ranking methods are investigated for simultaneous assessment of multiple measures of model quality for selecting tuning parameter values. One is a supervised learning fusion rule named sum of ranking differences (SRD). The other two are non-supervised learning processes based on the sum and median operations. The effect of the number of models evaluated on the three fusion rules are also evaluated using three procedures. One procedure uses all models from all possible combinations of the tuning parameters. To reduce the number of models evaluated, an iterative process (only applicable to SRD) is applied and thresholding a model quality measure before applying the fusion rules is also used. A near infrared pharmaceutical data set requiring model updating is used to evaluate the three fusion rules. In this case, calibration of the primary conditions is for the active pharmaceutical ingredient (API) of tablets produced in a laboratory. The secondary conditions for calibration updating is for tablets produced in the full batch setting. Two model updating processes requiring selection of two unique tuning parameter values are studied. One is based on Tikhonov regularization (TR) and the other is a variation of partial least squares (PLS). The three fusion methods are shown to provide equivalent and acceptable results allowing automatic selection of the tuning parameter values. Best tuning parameter values are selected when model quality measures used with the fusion rules are for the small secondary sample set used to form the updated models. In this model updating situation, evaluation of all possible models, thresholding, and iterative SRD performed equivalently for the three fusion rules with TR and PLS performed worse. While the application is model updating, the fusion processes are applicable to other situations requiring selection of multiple tuning parameter values.

Sum of ranking differences (SRD) to ensemble multivariate calibration model merits for tuning parameter selection and comparing calibration methods.

Most multivariate calibration methods require selection of tuning parameters, such as partial least squares (PLS) or the Tikhonov regularization variant ridge regression (RR). Tuning parameter values determine the direction and magnitude of respective model vectors thereby setting the resultant predication abilities of the model vectors. Simultaneously, tuning parameter values establish the corresponding bias/variance and the underlying selectivity/sensitivity tradeoffs. Selection of the final tuning parameter is often accomplished through some form of cross-validation and the resultant root mean square error of cross-validation (RMSECV) values are evaluated. However, selection of a "good" tuning parameter with this one model evaluation merit is almost impossible. Including additional model merits assists tuning parameter selection to provide better balanced models as well as allowing for a reasonable comparison between calibration methods. Using multiple merits requires decisions to be made on how to combine and weight the merits into an information criterion. An abundance of options are possible. Presented in this paper is the sum of ranking differences (SRD) to ensemble a collection of model evaluation merits varying across tuning parameters. It is shown that the SRD consensus ranking of model tuning parameters allows automatic selection of the final model, or a collection of models if so desired. Essentially, the user's preference for the degree of balance between bias and variance ultimately decides the merits used in SRD and hence, the tuning parameter values ranked lowest by SRD for automatic selection. The SRD process is also shown to allow simultaneous comparison of different calibration methods for a particular data set in conjunction with tuning parameter selection. Because SRD evaluates consistency across multiple merits, decisions on how to combine and weight merits are avoided. To demonstrate the utility of SRD, a near infrared spectral data set and a quantitative structure activity relationship (QSAR) data set are evaluated using PLS and RR.

Feasibility study for transforming spectral and instrumental artifacts for multivariate calibration maintenance.

Frequently, a spectral-based multivariate calibration model formed on a particular instrument (primary) needs to predict samples measured on other (secondary) instruments of the same spectral type. This situation is often referred to as calibration maintenance or transfer. A new calibration maintenance approach is developed in this paper using spectral differences between instruments. In conjunction with a sample weighting scheme, spectral differences are piecewise (wavelength window) or full spectrum fitted with modeling terms (correction terms) such as polynomials and derivatives. Results demonstrating the potential usefulness of the new method using a near infrared (NIR) benchmark dataset are presented in this paper. The process does not need a standardization sample set measured in the primary condition. Thus, the new approach is a "hybrid" between the popular methods of extended inverted multiplicative signal correction (EISC) and direct standardization (DS) or piecewise DS (PDS). It is found that prediction errors reduce for samples measured in the secondary condition compared to those based on no calibration transfer. Prediction errors are also comparable to those from a full calibration in the secondary condition. In addition to instrument correction, an extension of the new approach is discussed (but not tested) for predicting new samples changing over time due to new chemical, physical, and environmental measurement conditions including individually or combinations of temperature, sample particle size, and new spectrally responding species.

Data fusion for food authentication. Combining rare earth elements and trace metals to discriminate "Fava Santorinis" from other yellow split peas using chemometric tools.

"Fava Santorinis", is a protected designation of origin (PDO) yellow split pea species growing only in the island of Santorini in Greece. Due to its nutritional quality and taste, it has gained a high monetary value. Thus, it is prone to adulteration with other yellow split peas. In order to discriminate "Fava Santorinis" from other yellow split peas, four classification methods utilising rare earth elements (REEs) measured through inductively coupled plasma-mass spectrometry (ICP-MS) are studied. The four classification processes are orthogonal projection analysis (OPA), Mahalanobis distance (MD), partial least squares discriminant analysis (PLS-DA) and k nearest neighbours (KNN). Since it is known that trace elements are often useful to determine geographical origin of food products, we further quantitated for trace elements using ICP-MS. Presented in this paper are results using the four classification processes based on the fusion of the REEs data with the trace element data. Overall, the OPA method was found to perform best with up to 100% accuracy using the fused data.

Food adulteration analysis without laboratory prepared or determined reference food adulterant values.

Quantitative analysis of food adulterants is an important health and economic issue that needs to be fast and simple. Spectroscopy has significantly reduced analysis time. However, still needed are preparations of analyte calibration samples matrix matched to prediction samples which can be laborious and costly. Reported in this paper is the application of a newly developed pure component Tikhonov regularization (PCTR) process that does not require laboratory prepared or reference analysis methods, and hence, is a greener calibration method. The PCTR method requires an analyte pure component spectrum and non-analyte spectra. As a food analysis example, synchronous fluorescence spectra of extra virgin olive oil samples adulterated with sunflower oil is used. Results are shown to be better than those obtained using ridge regression with reference calibration samples. The flexibility of PCTR allows including reference samples and is generic for use with other instrumental methods and food products.

Spectral multivariate calibration without laboratory prepared or determined reference analyte values.

An essential part to calibration is establishing the analyte calibration reference samples. These samples must characterize the sample matrix and measurement conditions (chemical, physical, instrumental, and environmental) of any sample to be predicted. Calibration usually requires measuring spectra for numerous reference samples in addition to determining the corresponding analyte reference values. Both tasks are typically time-consuming and costly. This paper reports on a method named pure component Tikhonov regularization (PCTR) that does not require laboratory prepared or determined reference values. Instead, an analyte pure component spectrum is used in conjunction with nonanalyte spectra for calibration. Nonanalyte spectra can be from different sources including pure component interference samples, blanks, and constant analyte samples. The approach is also applicable to calibration maintenance when the analyte pure component spectrum is measured in one set of conditions and nonanalyte spectra are measured in new conditions. The PCTR method balances the trade-offs between calibration model shrinkage and the degree of orthogonality to the nonanalyte content (model direction) in order to obtain accurate predictions. Using visible and near-infrared (NIR) spectral data sets, the PCTR results are comparable to those obtained using ridge regression (RR) with reference calibration sets. The flexibility of PCTR also allows including reference samples if such samples are available.

Updating a near-infrared multivariate calibration model formed with lab-prepared pharmaceutical tablet types to new tablet types in full production.

Determining active pharmaceutical ingredient (API) tablet concentrations rapidly and efficiently is of great importance to the pharmaceutical industry in order to assure quality control. Using near-infrared (NIR) spectra measured on tablets in conjunction with multivariate calibration has been shown to meet these objectives. However, the calibration is typically developed under one set of conditions (primary conditions) and new tablets are produced under different measurement conditions (secondary conditions). Hence, the accuracy of multivariate calibration is limited due to differences between primary and secondary conditions such as tablet variances (composition, dosage, and production processes and precision), different instruments, and/or new environmental conditions. This study evaluates application of Tikhonov regularization (TR) to update NIR calibration models developed in a controlled primary laboratory setting to predict API tablet concentrations manufactured in full production where conditions and tablets are significantly different than in the laboratory. With just a few new tablets from full production, it is found that TR provides reduced prediction errors by as much as 64% in one situation compared to no model-updating. TR prediction errors are reduced by as much as 51% compared to local centering, another calibration maintenance method. The TR updated primary models are also found to predict as well as a full calibration model formed in the secondary conditions.

Updating a synchronous fluorescence spectroscopic virgin olive oil adulteration calibration to a new geographical region.

Detecting and quantifying extra virgin olive adulteration is of great importance to the olive oil industry. Many spectroscopic methods in conjunction with multivariate analysis have been used to solve these issues. However, successes to date are limited as calibration models are built to a specific set of geographical regions, growing seasons, cultivars, and oil extraction methods (the composite primary condition). Samples from new geographical regions, growing seasons, etc. (secondary conditions) are not always correctly predicted by the primary model due to different olive oil and/or adulterant compositions stemming from secondary conditions not matching the primary conditions. Three Tikhonov regularization (TR) variants are used in this paper to allow adulterant (sunflower oil) concentration predictions in samples from geographical regions not part of the original primary calibration domain. Of the three TR variants, ridge regression with an additional 2-norm penalty provides the smallest validation sample prediction errors. Although the paper reports on using TR for model updating to predict adulterant oil concentration, the methods should also be applicable to updating models distinguishing adulterated samples from pure extra virgin olive oil. Additionally, the approaches are general and can be used with other spectroscopic methods and adulterants as well as with other agriculture products.