Joan Ferré

Transfer of multivariate calibration models: a review

Multivariate calibration models are of critical importance to many analytical measurements, particularly for spectroscopic data. Generally, considerable effort is placed into constructing a robust model since it is meant to be used for extended periods of time. A problem arises, though, when the samples to be predicted are measured on a different instrument or under differing environmental factors from those used to build the model. The changes in spectral variations between the two conditions may make the model invalid for prediction in the new system. Various standardization and preprocessing methods have been developed to enable a calibration model to be effectively transferred between two systems, thus eliminating the need for a full recalibration. This paper presents an overview of the different methods used for calibration transfer and a critical assessment of their validity and applicability. The focus is on methods for transfer of near-infrared (NIR) spectra.

Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report)

This paper gives an introduction to multivariate calibration from a chemometrics perspective and reviews the various proposals to generalize the well-established univariate methodology to the multivariate domain. Univariate calibration leads to relatively simple models with a sound statistical underpinning. The associated uncertainty estimation and figures of merit are thoroughly covered in several official documents. However, univariate model predictions for unknown samples are only reliable if the signal is sufficiently selective for the analyte of interest. By contrast, multivariate calibration methods may produce valid predictions also from highly unselective data. A case in point is quantification from near-infrared (NIR) spectra. With the ever-increasing sophistication of analytical instruments inevitably comes a suite of multivariate calibration methods, each with its own underlying assumptions and statistical properties. As a result, uncertainty estimation and figures of merit for multivariate calibration methods has become a subject of active research, especially in the field of chemometrics.

Data fusion methodologies for food and beverage authentication and quality assessment – A review

The ever increasing interest of consumers for safety, authenticity and quality of food commodities has driven the attention towards the analytical techniques used for analyzing these commodities. In recent years, rapid and reliable sensor, spectroscopic and chromatographic techniques have emerged that, together with multivariate and multiway chemometrics, have improved the whole control process by reducing the time of analysis and providing more informative results. In this progression of more and better information, the combination (fusion) of outputs of different instrumental techniques has emerged as a means for increasing the reliability of classification or prediction of foodstuff specifications as compared to using a single analytical technique. Although promising results have been obtained in food and beverage authentication and quality assessment, the combination of data from several techniques is not straightforward and represents an important challenge for chemometricians. This review provides a general overview of data fusion strategies that have been used in the field of food and beverage authentication and quality assessment.

Net analyte signal calculation for multivariate calibration

Abstract A unifying framework for calibration and prediction in multivariate calibration is shown based on the concept of the net analyte signal (NAS). From this perspective, the calibration step can be regarded as the calculation of a net sensitivity vector, whose length is the amount of net signal when the value of the property of interest (e.g. analyte concentration) is equal to unity. The prediction step can be interpreted as projecting a measured spectrum onto the direction of the net sensitivity vector. The length of the projected spectrum divided by the length of the net sensitivity vector is the predicted value of the property of interest. This framework, which is equivalent to the univariate calibration approach, is used for critically revising different definitions of NAS and their calculation methods. The framework is particularized for the classical least squares (CLS), principal component regression (PLS) and partial least-squares (PCR) regression models.

Limit of detection estimator for second-order bilinear calibration

A new approach is developed for estimating the limit of detection in second-order bilinear calibration with the generalized rank annihilation method (GRAM). The proposed estimator is based on recently derived expressions for prediction variance and bias. It follows the latest IUPAC recommendations in the sense that it concisely accounts for the probabilities of committing both types I and II errors, i.e. false positive and false negative declarations, respectively. The estimator has been extensively validated with simulated data, yielding promising results.

Rapid characterization of transgenic and non-transgenic soybean oils by chemometric methods using NIR spectroscopy

Near infrared (NIR) spectroscopy and multivariate classification were applied to discriminate soybean oil samples into non-transgenic and transgenic. Principal Component Analysis (PCA) was applied to extract relevant features from the spectral data and to remove the anomalous samples. The best results were obtained when with Support Vectors Machine-Discriminant Analysis (SVM-DA) and Partial Least Squares-Discriminant Analysis (PLS-DA) after mean centering plus multiplicative scatter correction. For SVM-DA the percentage of successful classification was 100% for the training group and 100% and 90% in validation group for non transgenic and transgenic soybean oil samples respectively. For PLS-DA the percentage of successful classification was 95% and 100% in training group for non transgenic and transgenic soybean oil samples respectively and 100% and 80% in validation group for non transgenic and transgenic respectively. The results demonstrate that NIR spectroscopy can provide a rapid, nondestructive and reliable method to distinguish non-transgenic and transgenic soybean oils.

Second-order bilinear calibration: the effects of vectorising the data matrices of the calibration set

In a groundbreaking paper, Linder and Sundberg [Chemometr. Intell. Lab. Syst. 42 (1998) 159] developed a statistical framework for the calibration of second-order bilinear data. Within this framework, they formulated three different predictor construction methods [J. Chemom. 16 (2002) 12], namely the so-called naive method, the bilinear least squares (BLLS) method, and a refined version of the latter that takes account of the calibration uncertainty. Elsewhere [J. Chemom. 15 (2001) 743], a close relationship is established between the naive method and the generalized rank annihilation method (GRAM) by comparing expressions for prediction variance. Here it is proved that the BLLS method can be interpreted to work with vectorised data matrices, which establishes an algebraic relationship with so-called unfold partial least squares (PLS) and unfold principal component regression (PCR). It is detailed how these results enable quantifying the effects of vectorising bilinear second-order data matrices on analytical figures of merit and variance inflation factors.

Quantifying selectivity in spectrophotometric multicomponent analysis

Abstract According to the latest recommendation of the International Union of Pure and Applied Chemistry, “selectivity refers to the extent to which the method can be used to determine particular analytes in mixtures or matrices without interferences from other components of similar behavior”. Because of the prime importance of selectivity as an analytical figure of merit, numerous proposals have been published on how to quantify it in spectrophotometric multicomponent analysis. We show that the criterion independently developed by Lorber [11,12] and Bergmann, von Oepen and Zinn [13] is the most suitable, because it directly relates to prediction uncertainty and allows for a consistent generalization to more complex systems of chemical analysis.

Time shift correction in second-order liquid chromatographic data with iterative target transformation factor analysis

Abstract When the generalized rank annihilation method (GRAM) is applied to liquid chromatographic data with diode-array detection, an important problem is the time shift of the peak of the analyte in the test sample. This problem leads to erroneous predictions. This time shift can be corrected if a time window is selected so that the chromatographic profile of the analyte in the test sample is trilinear with the peak of the analyte in the calibration sample. In this paper we present a new method to determine when this condition is met. This method is based on the curve resolution with iterative target transformation factor analysis (ITTFA). The calibration and test matrices are independently decomposed into profiles and spectra, and aligned before GRAM is applied. Here we study two situations: first, when the calibration matrix has one analyte and second, when it has two analytes. When the calibration matrix has two analytes, we selectively determine the time window for the analyte to be quantified. There were considerably fewer prediction errors after correction.

Using second-order calibration to identify and quantify aromatic sulfonates in water by high-performance liquid chromatography in the presence of coeluting interferences

We used the Generalized Rank Annihilation Method (GRAM), a second-order calibration method, to quantify aromatic sulfonates in water with high-performance liquid chromatography (HPLC) when interferences coeluted with the analytes of interest. With GRAM, we can quantify in only two chromatographic analyses, one for a calibration sample and one for the unknown sample. The calculated concentrations were not statistically different to those obtained when the chromatographic separation of the unknown sample was modified in order to completely separate the analyte from the interferences before univariate calibration. With GRAM, the concentrations are determined much more quickly because a complete resolution is not required.