Variable selection by modified IPW (iterative predictor weighting)-PLS (partial least squares) in continuous wavelet regression models

Variable selection is often used to produce more robust and parsimonious regression models. But when they are applied directly to the raw near-infrared spectra, it is not easy to select appropriate variables because background and noise will often overshadow or overlap the absorption bands of analyte. In this work, a new hybrid algorithm based on the selection of the most informative variables in the continuous wavelet transform (CWT) domain is described. The strategy is a combination of CWT and a procedure of modified iterative predictor weighting-partial least square (mIPW-PLS). After elimination of the background and noise in NIR spectra by CWT, the mIPW-PLS approach is used to select the most informative CWT coefficients. With the selected CWT coefficients, a PLS model is built finally for prediction. It is indicated that the extraction of most important variables in the CWT domain can effectively avoid the interference of background and noise, and result in a high quality of regression model with a very small number of variables and fewer PLS components.     

An adaptive strategy for selecting representative calibration samples in the continuous wavelet domain for near-infrared spectral analysis

Sample selection is often used to improve the cost-effectiveness of near-infrared (NIR) spectral analysis. When raw NIR spectra are used, however, it is not easy to select appropriate samples, because of background interference and noise. In this paper, a novel adaptive strategy based on selection of representative NIR spectra in the continuous wavelet transform (CWT) domain is described. After pretreatment with the CWT, an extension of the Kennard–Stone (EKS) algorithm was used to adaptively select the most representative NIR spectra, which were then submitted to expensive chemical measurement and multivariate calibration. With the samples selected, a PLS model was finally built for prediction. It is of great interest to find that selection of representative samples in the CWT domain, rather than raw spectra, not only effectively eliminates background interference and noise but also further reduces the number of samples required for a good calibration, resulting in a high-quality regression model that is similar to the model obtained by use of all the samples. The results indicate that the proposed method can effectively enhance the cost-effectiveness of NIR spectral analysis. The strategy proposed here can also be applied to different analytical data for multivariate calibration.     

A new hybrid strategy for constructing a robust calibration model for near-infrared spectral analysis

A new hybrid algorithm is proposed for construction of a high-quality calibration model for near-infrared (NIR) spectra that is robust against both spectral interference (including background and noise) and multiple outliers. The algorithm is a combination of continuous wavelet transform (CWT) and a modified iterative reweighted PLS (mIRPLS) procedure. In the proposed algorithm the spectral interference is filtered by CWT at the first stage then mIRPLS is proposed to detect the multiple outliers in the CWT domain. Compared with the original IRPLS method, mIRPLS does not need to adjust variable parameters to achieve optimum calibration results, which makes it very convenient to perform in practice. The final PLS model is constructed robustly because both the spectral interference and multiple outliers are eliminated. In order to validate the effectiveness and universality of the algorithm, it was applied to two different sets of NIR spectra. The results indicate that the proposed strategy can greatly enhance the robustness and predictive ability of NIR spectral analysis.     

Elimination of interference information by a new hybrid algorithm for quantitative calibration of near infrared spectra

A new hybrid algorithm is proposed to eliminate the interference information for multivariate calibration of near-infrared (NIR) spectra that includes noise, background and systemic spectral variation irrelevant to concentration. The method consists of two parts: approximate derivative based on continuous wavelet transform (CWT) and orthogonal signal correction (OSC). After the approximate derivative calculated by CWT, OSC was performed. It was successfully applied to real complex NIR spectral data to eliminate the interference information. Correction for the interference of NIR spectra resulted in a substantial improvement in the predicted precision, and a more concise calibration model was obtained. The proposed procedure also compared favourably with several pretreatment methods, and the new method appears to provide a high-performance pretreatment tool for multivariate calibration of NIR spectra. In addition, the strategy proposed here can be applied to various other spectral data for quantitative purposes as well.     

Determination of chlorogenic acid in plant samples by using near-infrared spectrum with wavelet transform preprocessing.

By theoretical analysis, it is found that wavelet transform (WT) with a wavelet function can be regarded as a smoothing and a differentiation process, and that the order of differentiation is determined by the vanishing moment, which is an important property of a wavelet function. Therefore, a method based on the continuous wavelet transform (CWT) for removing the background in the near-infrared (NIR) spectrum is proposed, and it is used in the determination of the chlorogenic acid in plant samples as a preprocessing tool for partial least square (PLS) modeling. It is shown that the benefit of the proposed method lies not only in its performance to improve the quality of PLS model and the prediction precision, but also in its simplicity and practicability. It may become a convenient and efficient tool for preprocessing NIR spectral data sets in multivariate calibration.     

Wavelet unfolded partial least squares for near-infrared spectral quantitative analysis of blood and tobacco powder samples

Continuous wavelet transform (CWT) has been shown to be a high-performance signal processing technique in multivariate calibration. However, the signal processed by CWT with a specific wavelet may account for only a part of the information. To effectively utilize more abundant information contained in analytical signals, a method, named as wavelet unfolded partial least squares (WUPLS), was proposed. In the approach, the measured dataset is firstly extended by CWT with different wavelets, and then partial least squares (PLS) is employed to develop the quantitative model between the extended dataset and the target values. In order to select the representative wavelets, principal component analysis (PCA) is used to investigate the distribution of the signals obtained by CWT with different wavelets. The performance of the method was tested with blood and tobacco powder samples. Compared with the results obtained by PLS methods, the WUPLS method combined with signal processing techniques is proven to be a promising tool for improving the near-infrared (NIR) spectral analysis of complex samples.     

Key wavelengths screening using competitive adaptive reweighted sampling method for multivariate calibration

By employing the simple but effective principle ‘survival of the fittest’ on which Darwin's Evolution Theory is based, a novel strategy for selecting an optimal combination of key wavelengths of multi-component spectral data, named competitive adaptive reweighted sampling (CARS), is developed. Key wavelengths are defined as the wavelengths with large absolute coefficients in a multivariate linear regression model, such as partial least squares (PLS). In the present work, the absolute values of regression coefficients of PLS model are used as an index for evaluating the importance of each wavelength. Then, based on the importance level of each wavelength, CARS sequentially selects N subsets of wavelengths from N Monte Carlo (MC) sampling runs in an iterative and competitive manner. In each sampling run, a fixed ratio (e.g. 80%) of samples is first randomly selected to establish a calibration model. Next, based on the regression coefficients, a two-step procedure including exponentially decreasing function (EDF) based enforced wavelength selection and adaptive reweighted sampling (ARS) based competitive wavelength selection is adopted to select the key wavelengths. Finally, cross validation (CV) is applied to choose the subset with the lowest root mean square error of CV (RMSECV). The performance of the proposed procedure is evaluated using one simulated dataset together with one near infrared dataset of two properties. The results reveal an outstanding characteristic of CARS that it can usually locate an optimal combination of some key wavelengths which are interpretable to the chemical property of interest. Additionally, our study shows that better prediction is obtained by CARS when compared to full spectrum PLS modeling, Monte Carlo uninformative variable elimination (MC-UVE) and moving window partial least squares regression (MWPLSR).     

Rapid Determination of Metabolites in Bio‐fluid Samples by Raman Spectroscopy and Optimum Combinations of Chemometric Methods

The application of Raman spectroscopic techniques combined with multivariate chemometrics signal processing promise new means for the rapid multidimensional analysis of metabolites non‐destructively, with little or no sample preparation and little sensitivity to water. However, Rayleigh scattering, fluorescence and uncontrolled variance present substantial challenges for the accurate quantitative analysis of metabolites at physiological levels in biologically varying samples. Effective strategies include the application of chemometrics pretreatments for reducing Raman spectral interference. However, the arbitrary application of individual or combined pretreatment procedures can significantly alter the outcome of a measurement, thereby complicating spectral analysis. This paper evaluates and compares six signal pretreatment methods for correcting the baseline variances, together with three variable selection methods for eliminating uninformative variables, all within the context of multivariate calibration models based on partial least squares (PLS) regression. Raman spectra of 90 artificial bio‐fluid samples with eight urine metabolites at near‐physiological concentrations were used to test these models. The combination of multiplicative scatter correction (MSC), continuous wavelet transform (CWT), randomization test (RT) and PLS modeling presented the best performance for all the metabolites. The correlation coefficient (R) between predicted and prepared concentration reached as high as 0.96.     

Orthogonal projection to latent structures solution properties for chemometrics and systems biology data

Partial least squares (PLS) is a widely used algorithm in the field of chemometrics. In calibration studies, a PLS variant called orthogonal projection to latent structures (O‐PLS) has been shown to successfully reduce the number of model components while maintaining good prediction accuracy, although no theoretical analysis exists demonstrating its applicability in this context. Using a discrete formulation of the linear mixture model known as Beer's law, we explicitly analyze O‐PLS solution properties for calibration data. We find that, in the absence of noise and for large n, O‐PLS solutions are simpler but just as accurate as PLS solutions for systems in which analyte and background concentrations are uncorrelated. However, the same is not true for the most general chemometric data in which correlations between the analyte and background concentrations are nonzero and pure profiles overlap. On the contrary, forcing the removal of orthogonal components may actually degrade interpretability of the model. This situation can also arise when the data are noisy and n is small, because O‐PLS may identify and model the noise as orthogonal when it is statistically uncorrelated with the analytes. For the types of data arising from systems biology studies, in which the number of response variables may be much greater than the number of observations, we show that O‐PLS is unlikely to discover orthogonal variation whether or not it exists. In this case, O‐PLS and PLS solutions are the same. Copyright © 2011 John Wiley & Sons, Ltd.     

Continuous wavelet transform applied to removing the fluctuating background in near-infrared spectra

A novel method based on continuous wavelet transform (CWT) was proposed as a preprocessing tool for the near-infrared (NIR) spectra. Due to the property of the vanishing moments of the wavelet, the fluctuating background of the NIR spectra can be successfully removed through convolution of the spectra with an appropriate wavelet function. The vanishing moments of a wavelet and the scale parameter are two key factors that govern the result of the background elimination. The result of its application to both the simulated spectra and the NIR spectra of tobacco samples demonstrates that CWT is a competitive tool for removing fluctuating background in spectra.     

An ensemble method based on a self-organizing map for near-infrared spectral calibration of complex beverage samples

Based on a so-called ensemble strategy, an algorithm is proposed for near-infrared (NIR) spectral calibration of complex beverage samples. This algorithm is a combination of a novel training set/test set sample-selection procedure based on a Kohonen self-organizing map (SOM) with a simple procedure to calculate an average partial least-squares (PLS) calibration model, which is therefore named SOMEPLS. In order to verify the proposed SOMEPLS, two NIR beverage datasets involving the determination of sugar content are considered, and three kinds of reference algorithm, i.e., conventional PLS (CPLS), the Kennard-Stone (KS) algorithm in combination with PLS (KSPLS), and sample set partitioning based on the joint x-y distance (SPXY) algorithm in combination with PLS (SPXYPLS), are used. Of these, both KS and SPXY are well-known representative sample-selection algorithms. By comparison, it was found that when there is a training set of appropriate size, SOMEPLS can achieve better prediction accuracy than the three reference algorithms, but without increasing the complexity of the corresponding calibration model for the future application, indicating that SOMEPLS can serve as a promising tool for NIR spectral calibration.     

A partial least squares and wavelet-transform hybrid model to analyze carbon content in coal using laser-induced breakdown spectroscopy

A partial least squares (PLS) and wavelet transform hybrid model are proposed to analyze the carbon content of coal by using laser-induced breakdown spectroscopy (LIBS). The hybrid model is composed of two steps of wavelet analysis procedures, which include environmental denoising and background noise reduction, to pretreat the LIBS spectrum. The processed wavelet coefficients, which contain the discrete line information of the spectra, were taken as inputs for the PLS model for calibration and prediction of carbon element. A higher signal-to-noise ratio of carbon line was obtained after environmental denoising, and the best decomposition level was determined after background noise reduction. The hybrid model resulted in a significant improvement over the conventional PLS method under different ambient environments, which include air, argon, and helium. The average relative error of carbon decreased from 2.74 to 1.67% under an ambient helium environment, which indicated a significantly improved accuracy in the measurement of carbon in coal. The best results obtained under an ambient helium environment could be partly attributed to the smallest interference by noise after wavelet denoising. A similar improvement was observed in ambient air and argon environments, thereby proving the applicability of the hybrid model under different experimental conditions.     

离子液体吸附剂对木犀草素的富集及CARS变量筛选的近红外光谱分析方法

该文以咪唑型离子液体作为原料制备吸附剂富集稀溶液中的木犀草素,利用竞争性自适应权重(CARS)变量筛选的方法建立了一种快速测定木犀草素的近红外光谱分析方法。考察了吸附剂用量、pH值、振荡时间对吸附效果的影响,并探究了吸附剂的吸附能力;富集木犀草素的吸附剂经近红外漫反射光谱检测,采用CARS变量筛选的方法结合偏最小二乘回归(PLS)建立了木犀草素的定量校正模型。结果表明,吸附剂用量为0.15 g、pH值为7、振荡时间为20 min的最佳条件下,吸附率达90.9%,且该吸附符合Langmuir等温吸附模型,最大吸附量为7.1 mg/g。近红外光谱建模中,与未经CARS变量筛选处理作为对照,对比发现经CARS变量筛选的方法结果更优,并采用连续小波变换(CWT)的光谱预处理进行验证,结果表明经CWT处理后,预测残差(RPD)值增大,说明了模型的可靠性。该方法可有效富集稀溶液中的木犀草素,采用CARS变量筛选结合CWT光谱预处理的近红外光谱方法可实现对稀溶液中木犀草素的灵敏、快捷检测。     

独立分量分析预处理法提高苹果糖度模型预测精度研究

为了提高苹果近红外光谱糖度预测模型精度,利用独立分量分析方法(ICA)对苹果近红外光谱进行了预处理,并且建立了糖度的偏最小二乘(PLS)预测模型。结果表明,独立分量分析不但能分离出噪声信号,而且所分离出来的光谱信号也比原始光谱信号光滑。在预处理后的最佳PLS糖度模型校正时的相关系数rc和标准偏差SEC分别为0.9549和0.3361,用于预测时的相关系数rp和标准偏差SEP分别为0.9071和0.4355。与普通的平均处理法的PLS模型相比,其精度有所提高,且模型更加简洁。     

A wavelength selection method based on random decision particle swarm optimization with attractor for near‐infrared spectral quantitative analysis

In this paper, we proposed a wavelength selection method based on random decision particle swarm optimization with attractor for near‐infrared (NIR) spectra quantitative analysis. The proposed method was incorporated with partial least square (PLS) to construct a prediction model. The proposed method chooses the current own optimal or the current global optimal to calculate the attractor. Then the particle updates its flight velocity by the attractor, and the particle state is updated by the random decision with the new velocity. Moreover, the root‐mean‐square error of cross‐validation is adopted as the fitness function for the proposed method. In order to demonstrate the usefulness of the proposed method, PLS with all wavelengths, uninformative variable elimination by PLS, elastic net, genetic algorithm combined with PLS, the discrete particle swarm optimization combined with PLS, the modified particle swarm optimization combined with PLS, the neighboring particle swarm optimization combined with PLS, and the proposed method are used for building the components quantitative analysis models of NIR spectral datasets, and the effectiveness of these models is compared. Two application studies are presented, which involve NIR data obtained from an experiment of meat content determination using NIR and a combustion procedure. Results verify that the proposed method has higher predictive ability for NIR spectral data and the number of selected wavelengths is less. The proposed method has faster convergence speed and could overcome the premature convergence problem. Furthermore, although improving the prediction precision may sacrifice the model complexity under a certain extent, the proposed method is overfitted slightly. Copyright © 2015 John Wiley & Sons, Ltd.     

Qualitative and quantitative analysis of oxytetracycline by near-infrared spectroscopy

Near-infrared (NIR) spectroscopy, in combination with chemometrics, enable the analysis of raw materials without time-consuming sample preparation methods. The aim of our work was to estimate critical parameters in the analytical specification of oxytetracycline, and consequently the development of a method for quantification and qualification of these parameters by NIR spectroscopy. A Karl Fischer (K.F.) titration to determine the water content, a colorimetric assay method, and Fourier transform-infrared (FT-IR) spectroscopy to identify the oxytetracycline base, were used as reference methods, respectively. Multivariate calibration was performed on NIR spectral data using principal component analysis (PCA), partial least-squares (PLS 1) and principal component regression (PCR) chemometric methods. Multivariate calibration models for NIR spectroscopy have been developed. Using PCA and the Soft Independent Modelling of Class Analogy (SIMCA) approach, we established the cluster model for the determination of sample identity. PLS 1 and PCR regression methods were applied to develop the calibration models for the determination of water content and the assay of the oxytetracycline base. Comparing the PLS and PCR regression methods we found out that the PLS is better established by NIR, especially as the spectroscopic data (NIR spectra) are highly collinear and there are many wavelengths due to non-selective wavelengths. The calibration models for NIR spectroscopy are convenient alternatives to the colorimetric method and to the K.F. method, as well as to FT-IR spectroscopy, in the routine control of incoming material.     

连续小波变换-独立成分回归算法及其在多组分分析中的应用

采用连续小波变换（CWT）对光谱数据进行处理，用独立成分分析（ICA）进行特征提取，再用回归分析方法对被测组分进行测定，建立了连续小波变换一独立成分回归（CWT-ICR）方法。方法用于肉样品中水分、脂肪和蛋白质多组分的同时测定，所得结果与化学法测得结果相符。     

A novel algorithm for linear multivariate calibration based on the mixed model of samples

We present a novel algorithm for linear multivariate calibration that can generate good prediction results. This is accomplished by the idea of that testing samples are mixed by the calibration samples in proper proportion. The algorithm is based on the mixed model of samples and is therefore called MMS algorithm. With both theoretical support and analysis of two data sets, it is demonstrated that MMS algorithm produces lower prediction errors than partial least squares (PLS2) model, has similar prediction performance to PLS1. In the anti-interference test of background, MMS algorithm performs better than PLS2. At the condition of the lack of some component information, MMS algorithm shows better robustness than PLS2.     

应用遗传算法和PLS的近红外光谱预测玉米中淀粉含量的研究

以普通玉米籽粒为试验材料,在应用遗传算法结合偏最小二乘回归法对近红外光谱数据进行特征波长选择的基础上,应用偏最小二乘回归法建立了特征波长测定玉米籽粒中淀粉含量的校正模型．试验结果表明,基于11个特征波长所建立的校正模型,其校正误差（RMSEC）、交叉检验误差（RMSECV）和预测误差（RMSEP）分别为0.30％、0.35％和0.27％,校正数据集和独立的检验数据集的预测值与实际测定值之间的相关系数分别达到0.9279和0.9390,与全光谱数据所建立的预测模型相比,在预测精度上均有所改善,表明应用遗传算法和PLS进行光谱特征选择,能获得更简单和更好的模型,为玉米籽粒中淀粉含量的近红外测定和红外光谱数据的处理提供了新的方法与途径．