Net Analyte Signal Vector Research Articles

Optimizing wavelength selection by using informative vectors for parsimonious infrared spectra modelling

Infrared spectroscopy has been widely adopted by various agricultural research. The typical spectra variables contain thousands of wavelengths. These large number of spectra variables often contribute to collinearity, and redundancies rather than relevant information. Variable selection of the predictors is an important step to create a robust calibration model from these spectra data. This paper presents an algorithm for spectra variable selection based on a combination of informative vectors and an ordered predictor selection (OPS) approach with an exponentially decreasing function (EDF) selection. Informative vectors are features derived from statistical principles that can be used to describe the relationship between the dependent variables and the predictors (spectra). The informative vectors analysed include regression coefficient vector (b), variable influence on projection (V), residual vector (S), net analyte signal vector (Na), linear correlation vector (COR), biweight mid-correlation vector (BIC), mutual information based on adjacency matrix (AMI), covariance procedures matrix (COV). These eight informative vectors can be joined in pairs and become 22 combination vectors. This approach was tested with near-infrared soil spectra for predicting the properties of pH, clay and sand content, cation exchange capacity (CEC), and total carbon content. This example used the Cubist regression tree and partial least squares regression (PLSR) models for calibration. By utilizing the subset of the spectra (retaining those that are significant based on the absolute values of the informative vectors), the regression models were still able to enhance the prediction capability. Overall, the PLSR model performed better than the Cubist model. The informative vector b (and its combinations) and S (and its combinations) were found to be the ones that provide the most accurate predictions for this dataset. Although the performance of the subset model does not perform better than the full spectra model, the number of wavelengths variable used in the model is significantly reduced to, on average, 25%.

An active learning representative subset selection method using net analyte signal

To guarantee accurate predictions, representative samples are needed when building a calibration model for spectroscopic measurements. However, in general, it is not known whether a sample is representative prior to measuring its concentration, which is both time-consuming and expensive. In this paper, a method to determine whether a sample should be selected into a calibration set is presented. The selection is based on the difference of Euclidean norm of net analyte signal (NAS) vector between the candidate and existing samples. First, the concentrations and spectra of a group of samples are used to compute the projection matrix, NAS vector, and scalar values. Next, the NAS vectors of candidate samples are computed by multiplying projection matrix with spectra of samples. Scalar value of NAS is obtained by norm computation. The distance between the candidate set and the selected set is computed, and samples with the largest distance are added to selected set sequentially. Last, the concentration of the analyte is measured such that the sample can be used as a calibration sample. Using a validation test, it is shown that the presented method is more efficient than random selection. As a result, the amount of time and money spent on reference measurements is greatly reduced.

Rapid Quantification of Melamine in Different Brands/Types of Milk Powders Using Standard Addition Net Analyte Signal and Near-Infrared Spectroscopy.

Multivariate calibration (MVC) and near-infrared (NIR) spectroscopy have demonstrated potential for rapid analysis of melamine in various dairy products. However, the practical application of ordinary MVC can be largely restricted because the prediction of a new sample from an uncalibrated batch would be subject to a significant bias due to matrix effect. In this study, the feasibility of using NIR spectroscopy and the standard addition (SA) net analyte signal (NAS) method (SANAS) for rapid quantification of melamine in different brands/types of milk powders was investigated. In SANAS, the NAS vector of melamine in an unknown sample as well as in a series of samples added with melamine standards was calculated and then the Euclidean norms of series standards were used to build a straightforward univariate regression model. The analysis results of 10 different brands/types of milk powders with melamine levels 0~0.12% (w/w) indicate that SANAS obtained accurate results with the root mean squared error of prediction (RMSEP) values ranging from 0.0012 to 0.0029. An additional advantage of NAS is to visualize and control the possible unwanted variations during standard addition. The proposed method will provide a practically useful tool for rapid and nondestructive quantification of melamine in different brands/types of milk powders.

Multivariate standard addition method solved by net analyte signal calculation and rank annihilation factor analysis

This article describes the use of the net analyte signal (NAS) concept and rank annihilation factor analysis (RAFA) for building two different multivariate standard addition models called "SANAS" and "SARAF." In the former, by the definition of a new subspace, the NAS vector of the analyte of interest in an unknown sample as well as the NAS vectors of samples spiked with various amounts of the standard solutions are calculated and then their Euclidean norms are plotted against the concentration of added standard. In this way, a simple linear standard addition graph similar to that in univariate calibration is obtained, from which the concentration of the analyte in the unknown sample and the analytical figures of merit are readily calculated. In the SARAF method, the concentration of the analyte in the unknown sample is varied iteratively until the contribution of the analyte in the response data matrix is completely annihilated. The proposed methods were evaluated by analyzing simulated absorbance data as well as by the analysis of two indicators in synthetic matrices as experimental data. The resultant predicted concentrations of unknown samples showed that the SANAS and SARAF methods both produced accurate results with relative errors of prediction lower than 5% in most cases.

The use of net analyte signal (NAS) in near infrared spectroscopy pharmaceutical applications: Interpretability and figures of merit

Near infrared spectroscopy (NIRS) has been extensively used as an analytical method for quality control of solid dosage forms for the pharmaceutical industry. Pharmaceutical formulations can be extremely complex, containing typically one or more active product ingredients (API) and various excipients, yielding very complex near infrared (NIR) spectra. The NIR spectra interpretability can be improved using the concept of net analyte signal (NAS). NAS is defined as the part of the spectrum unique to the analyte of interest. The objective of this work was to compare two different methods to estimate the API's NAS vector of different pharmaceutical formulations. The main difference between the methods is the knowledge of API free formulations NIR spectra. The comparison between the two methods was assessed in a qualitative and quantitative way. Results showed that both methods produced good results in terms of the similarity between the NAS vector and the pure API spectrum, as well as in the ability to predict the API concentration of unknown samples. Moreover, figures of merit such as sensitivity, selectivity, and limit of detection were estimated in a straightforward manner.

Net analyte signal-based simultaneous determination of antazoline and naphazoline using wavelength region selection by experimental design-neural networks

Net analyte signal (NAS)-based multivariate calibration methods were employed for simultaneous determination of anthazoline and naphazoline. The NAS vectors calculated from the absorbance data of the drugs mixture were used as input for classical least squares (CLS), principal component and partial least squares regression PCR and PLS methods. A wavelength selection strategy was used to find the best wavelength region for each drug separately. As a new procedure, we proposed an experimental design-neural network strategy for wavelength region optimization. By use of a full factorial design method, some different wavelength regions were selected by taking into account different spectral parameters including the starting wavelength, the ending wavelength and the wavelength interval. The performance of all the multivariate calibration methods, in all selected wavelength regions for both drugs, was evaluated by calculating a fitness function based on the root mean square error of calibration and validation. A three-layered feed-forward artificial neural network (ANN) model with back-propagation learning algorithm was employed to model the nonlinear relationship between the spectral parameters and fitness of each regression method. From the resulted ANN models, the spectral regions in which lowest fitness could be obtained were chosen. Comparison of the results revealed that the net NAS-PLS resulted in lower prediction error than the other models. The proposed NAS-based calibration method was successfully applied to the simultaneous analyses of anthazoline and naphazoline in a commercial eye drop sample.

The prediction error in CLS and PLS: the importance of feature selection prior to multivariate calibration

AbstractClassical least squares (CLS) and partial least squares (PLS) are two common multivariate regression algorithms in chemometrics. This paper presents an asymptotically exact mathematical analysis of the mean squared error of prediction of CLS and PLS under the linear mixture model commonly assumed in spectroscopy. For CLS regression with a very large calibration set the root mean squared error is approximately equal to the noise per wavelength divided by the length of the net analyte signal vector. It is shown, however, that for a finite training set with n samples in p dimensions there are additional error terms that depend on σ2p2/n2, where σ is the noise level per co‐ordinate. Therefore in the ‘large p—small n’ regime, common in spectroscopy, these terms can be quite large and even dominate the overall prediction error. It is demonstrated both theoretically and by simulations that dimensional reduction of the input data via their compact representation with a few features, selected for example by adaptive wavelet compression, can substantially decrease these effects and recover the asymptotic error. This analysis provides a theoretical justification for the need to perform feature selection (dimensional reduction) of the input data prior to application of multivariate regression algorithms. Copyright © 2005 John Wiley & Sons, Ltd.

Net analyte signal–artificial neural network (NAS–ANN) model for efficient nonlinear multivariate calibration

In recent years, artificial neural network (ANN) has been found major popularity in the analytical chemistry. This manuscript describes a simple and efficient ANN for modeling nonlinear spectral responses in spectroscopic multicomponent analyses. In this model, the spectral data were first subjected to net analyte signal (NAS) calculation and then the norm of the NAS vectors (||NAS||) was used as the input of the ANN model. Therefore, a simple model (NAS–ANN model) with only one node in input layer was obtained. A multilayer feed-forward neural network with back-propagation learning algorithm was used to process the nonlinear relationship between the ||NAS|| and concentration of analytes. The performance of the proposed model was evaluated by analysis of the simulated as well as the experimental data. In the simulated data, two source of nonlinearity including quadratic absorbance–concentration relationship and synergist effect were considered. In addition, the model was used for the simultaneous determination of three phenothiazine drugs including promethazine, chlorpromazine and perphenazine in their ternary mixture using conventional and derivative absorbance spectra. It was obtained that the proposed model could analyze the synthetic mixtures accurately. The model was compared with the PC–ANN model which is currently used for nonlinear multivariate calibration. The data confirmed that our model was simpler and produced more accurate results.

Partial least squares, Beer's law and the net analyte signal: statistical modeling and analysis

AbstractPartial least squares (PLS) is one of the most common regression algorithms in chemistry, relating input–output samples (xi, yi) by a linear multivariate model. In this paper we analyze the PLS algorithm under a specific probabilistic model for the relation between x and y. Following Beer's law, we assume a linear mixture model in which each data sample (x, y) is a random realization from a joint probability distribution where x is the sum of k components multiplied by their respective characteristic responses, and each of these components is a random variable. We analyze PLS on this model under two idealized settings: one is the ideal case of noise‐free samples and the other is the case of an infinite number of noisy training samples. In the noise‐free case we prove that, as expected, the regression vector computed by PLS is, up to normalization, the net analyte signal. We prove that PLS computes this vector after at most k iterations, where k is the total number of components. In the case of an infinite training set corrupted by unstructured noise, we show that PLS computes a final regression vector which is not in general purely proportional to the net analyte signal vector, but has the important property of being optimal under a mean squared error of prediction criterion. This result can be viewed as an asymptotic optimality of PLS in the limit of a very large but finite training set. Copyright © 2005 John Wiley & Sons, Ltd.

Discordance between net analyte signal theory and practical multivariate calibration.

Lorber's concept of net analyte signal is reviewed in the context of classical and inverse least-squares approaches to multivariate calibration. It is shown that, in the presence of device measurement error, the classical and inverse calibration procedures have radically different theoretical prediction objectives, and the assertion that the popular inverse least-squares procedures (including partial least squares, principal components regression) approximate Lorber's net analyte signal vector in the limit is disproved. Exact theoretical expressions for the prediction error bias, variance, and mean-squared error are given under general measurement error conditions, which reinforce the very discrepant behavior between these two predictive approaches, and Lorber's net analyte signal theory. Implications for multivariate figures of merit and numerous recently proposed preprocessing treatments involving orthogonal projections are also discussed.

Theory of net analyte signal vectors in inverse regression

AbstractThe net analyte signal and the net analyte signal vector are useful measures in building and optimizing multivariate calibration models. In this paper a theory for their use in inverse regression is developed. The theory of net analyte signal was originally derived from classical least squares in spectral calibration where the responses of all pure analytes and interferents are assumed to be known. However, in chemometrics, inverse calibration models such as partial least squares regression are more abundant and several tools for calculating the net analyte signal in inverse regression models have been proposed. These methods yield different results and most do not provide results that are in accordance with the chosen calibration model. In this paper a thorough development of a calibration‐specific net analyte signal vector is given. This definition turns out to be almost identical to the one recently suggested by Faber (Anal. Chem. 1998; 70: 5108–5110). A required correction of the net analyte signal in situations with negative predicted responses is also discussed. Copyright © 2004 John Wiley & Sons, Ltd.

Exact presentation of multivariate calibration model as univariate calibration graph

A proof is given that a recently introduced univariate presentation of a multivariate calibration model is exact, i.e., there are no approximations involved. The proof is based on: (1) previously proposed definitions of multivariate net analyte signal and multivariate calibration factors (sensitivity in classical model and inverse sensitivity in inverse model) and (2) the geometrical property of the true regression vector in inverse multivariate calibration that it must be proportional to the true multivariate net analyte signal vector of a particular sample. The extension of the proof to multiway calibration is briefly discussed. A practical example from near-infrared (NIR) spectroscopy is used to illustrate that the proposed univariate presentation may give more meaning to the term `spectral overlap'.

Mean centering and computation of scalar net analyte signal in multivariate calibration

Lorber has identified the net analyte signal (NAS) vector as the part of the gross signal which is orthogonal to the pure spectra of the interferents. For calculation of multivariate analytical figures of merit, such as sensitivity and signal-to-noise ratio, the NAS vector must be converted into a scalar NAS. The traditional methods for calculating the scalar NAS amount to taking the Euclidean norm of the NAS vector. For mean-centered data, straightforward implementation of this recipe leads to an artifact: one value for the scalar NAS corresponds to two values for analyte concentration, i.e. the conversion is not unique. This paper details the origin of the problem and proposes a simple solution. The improved calculation of scalar NAS is illustrated on the near-infrared prediction of weight per cent oxygen delivered by the oxygenate methyl tert-butyl ether in standard reference material gasoline ampoules. Copyright © 1998 John Wiley & Sons, Ltd.

Efficient Computation of Net Analyte Signal Vector in Inverse Multivariate Calibration Models

The net analyte signal vector has been defined by Lorber as the part of a mixture spectrum that is unique for the analyte of interest; i.e., it is orthogonal to the spectra of the interferences. It plays a key role in the development of multivariate analytical figures of merit. Applications have been reported that imply its utility for spectroscopic wavelength selection as well as calibration method comparison. Currently available methods for computing the net analyte signal vector in inverse multivariate calibration models are based on the evaluation of projection matrices. Due to the size of these matrices (p × p, with p the number of wavelengths) the computation may be highly memory- and time-consuming. This paper shows that the net analyte signal vector can be obtained in a highly efficient manner by a suitable scaling of the regression vector. Computing the scaling factor only requires the evaluation of an inner product (p multiplications and additions). The mathematical form of the newly derived expression is discussed, and the generalization to multiway calibration models is briefly outlined.