Independent component analysis and its applications in signal processing for analytical chemistry

Independent component analysis (ICA) is a statistical method the goal of which is to find a linear representation of non-Gaussian data so that the components are statistically independent, or as independent as possible. In an ICA procedure, the estimated independent components (ICs) are identical to or highly correlated to the spectral profiles of the chemical components in mixtures under certain circumstances, so the latent variables obtained are chemically interpretable and useful for qualitative analysis of mixtures without prior information about the sources or reference materials, and the calculated demixing matrix is useful for simultaneous determination of polycomponents in mixtures. We review commonly used ICA algorithms and recent ICA applications in signal processing for qualitative and quantitative analysis. Furthermore, we also review the preprocessing method for ICA applications and the robustness of different ICA algorithms, and we give the empirical criterion for selection of ICA algorithms in signal processing for analytical chemistry.     

Estimation of source spectra profiles and simultaneous determination of polycomponent in mixtures from ultraviolet spectra data using kernel independent component analysis and support vector regression

A method that use kernel independent component analysis (KICA) and support vector regression (SVR) was proposed for estimation of source ultraviolet (UV) spectra profiles and simultaneous determination of polycomponents in mixtures. In KICA-SVR procedure, the UV source spectra profiles were estimated using KICA, then the mixing matrix of the components were calculated using the estimated sources, and the calibration model was build using SVR based on the calculated mixing matrix. A simulated UV dataset of three-component mixtures was used to test the ability of KICA for estimating source spectra profiles from spectra data of mixtures. It was found that KICA has the potential power to estimate pure UV spectra profiles, and correlation coefficient of estimated sources correspond to the real adopted ones are better compared with that by FastICA and Infomax ICA. An UV dataset of polycomponent vitamin B was processed using the proposed KICA-SVR method. The results show that the estimated source spectra profiles are correlative with the real UV spectra of the components and chemically interpretable, and accurate results were obtained.     

基于独立分量和神经网络的近红外多组分分析方法

采用小波变换对光谱数据进行压缩,用独立分量分析(ICA)方法提取近红外光谱数据矩阵的独立成分和相应的混合矩阵,再用BP神经网络对混合矩阵和实测浓度矩阵进行建模,提出了基于独立分量分析-神经网络回归(ICA-NNR)的近红外分析建模方法。进一步研究了独立分量数和网络中间隐层的神经元数对模型性能的影响,经优化后的ICA-NNR模型在相关系数与均方根误差两个指标上均优于直接用光谱矩阵作为输入所建立的模型。本方法用于玉米中水分、淀粉、蛋白质3种主要成分含量的同时测定,检验样品集的化学检测值与近红外预测值的相关系数分别达到:淀粉r=0.971,蛋白质r=0.976,水分r=0.975。     

A new regression method based on independent component analysis

Based on independent component analysis (ICA), a new regression method, independent component regression (ICR), was developed to build the model of NIR spectra and the routine components of plant samples. It is found that ICR and principal component regression (PCR) are completely equivalent when they are applied in quantitative prediction. However, independent components (ICs) can give more chemical explanation than principal components (PCs) because independence is a high-order statistic that is a much stronger condition than orthogonality. Three ICs are obtained by ICA from the NIR spectra of plant samples; it is found that they are strongly correlated to the NIR spectra of water, hydrocarbons and organonitrogen compounds, respectively. Therefore, ICA may be a promising tool to retrieve both quantitative and qualitative information from complex chemical data sets.     

A new approach to near-infrared spectral data analysis using independent component analysis

This paper presents a new approach to near-infrared spectral (NIR) data analysis that is based on independent component analysis (ICA). The main advantage of the new method is that it is able to separate the spectra of the constituent components from the spectra of their mixtures. The separation is a blind operation, since the constituent components of mixtures can be unknown. The ICA based method is therefore particularly useful in identifying the unknown components in a mixture as well as in estimating their concentrations. The approach is introduced by reference to case studies and compared to other techniques for NIR analysis including principal component regression (PCR), multiple linear regression (MLR), and partial least squares (PLS) as well as Fourier and wavelet transforms.     

ICA方法与NIR技术用于药片中活性成分含量的测定

用独立分量分析(ICA)方法提取药片近红外光谱数据矩阵的独立成分和相应的混合矩阵, 再用BP神经网络对混合矩阵和药片中活性成分的浓度矩阵进行建模, 提出了新的药片活性成分含量测定的基于独立分量分析-神经网络回归(ICA-NNR)的近红外光谱分析方法. 通过分析独立分量数和网络中间隐层的神经元数对模型性能的影响, 分别建立三类药片定量分析的最优模型. 该方法用于实测的三类药片中活性成分含量的测定, 测试样品集的化学检测值与近红外预测值的相关系数分别达到0.962, 0.980及0.979. 结果表明, 基于ICA-NNR的近红外光谱分析方法对制药业的药片进行定量分析是可行的.     

Determination of effective wavelengths for discrimination of fruit vinegars using near infrared spectroscopy and multivariate analysis

Near infrared (NIR) spectroscopy based on effective wavelengths (EWs) and chemometrics was proposed to discriminate the varieties of fruit vinegars including aloe, apple, lemon and peach vinegars. One hundred eighty samples (45 for each variety) were selected randomly for the calibration set, and 60 samples (15 for each variety) for the validation set, whereas 24 samples (6 for each variety) for the independent set. Partial least squares discriminant analysis (PLS-DA) and least squares-support vector machine (LS-SVM) were implemented for calibration models. Different input data matrices of LS-SVM were determined by latent variables (LVs) selected by explained variance, and EWs selected by x-loading weights, regression coefficients, modeling power and independent component analysis (ICA). Then the LS-SVM models were developed with a grid search technique and RBF kernel function. All LS-SVM models outperformed PLS-DA model, and the optimal LS-SVM model was achieved with EWs (4021, 4058, 4264, 4400, 4853, 5070 and 5273 cm⁻¹) selected by regression coefficients. The determination coefficient (R²), RMSEP and total recognition ratio with cutoff value ±0.1 in validation set were 1.000, 0.025 and 100%, respectively. The overall results indicted that the regression coefficients was an effective way for the selection of effective wavelengths. NIR spectroscopy combined with LS-SVM models had the capability to discriminate the varieties of fruit vinegars with high accuracy.     

高光谱图像技术检测黄瓜叶片的叶绿素叶面分布

以黄瓜叶片为材料,利用高光谱图像技术结合独立分量法(ICA),研究了叶绿素浓度叶面分布的快速、无损检测方法.用高光谱相机采集了80片黄瓜叶子的高光谱图像(408～1117 nm),利用ICA方法提取了高光谱图像的8个独立分量信号,通过逐步线性回归(SMLR)优选出第1、第2和第5个ICA信号,并在此基础上建立了叶绿素浓...     

Cross validation and uncertainty estimates in independent component analysis

A data analysis tool, known as independent component analysis (ICA), is the main focus of this paper. The theory of ICA is briefly reviewed, and the underlying statistical assumptions and a practical algorithm are described. This paper introduces cross validation/jack-knifing and significance tests to ICA. Jack-knifing is applied to estimate uncertainties for the ICA loadings, which also serve as a basis for significance tests. These tests are shown to improve ICA performance, indicating how many components are mixed in the observed data, and also which parts of the extracted sources that contain significant information. We address the issue of stability for the ICA model through uncertainty plots. The ICA performance is compared to principal component analysis (PCA) for two selected applications, a simulated experiment and a real world application.     

Application of neural networks with novel independent component analysis methodologies for the simultaneous determination of cadmium,copper, and lead using an ISE array

The paper introduces a novel chemometric strategy based on independent component analysis (ICA) coupled with a back‐propagation neural network. In this approach, one of the most popular ICA methods, the fast fixed‐point algorithm for ICA (fastICA), was implemented by the genetic algorithm (geneticICA) to avoid the local maxima problem commonly observed with fastICA. As a case study, an ion‐selective electrode (ISE) array, consisting of three working electrodes and one reference electrode, was used for the simultaneous determination of three heavy metals (cadmium, copper, and lead) in aqueous solutions, which are normally prone to severe interferences. The robustness and appropriateness of the approach were assessed using the average mean of relative error (MRE) of triplicated external validation. After configuration and optimization, the average MRE for Cu was <5%. For the determination of Cd and Pb, whose ISEs normally cannot tolerate Cu ions even at the microgram per liter levels, the MREs were 8%. This article demonstrated that this approach can be applied to the detection of heavy metal contamination in industrial wastewater with prediction accuracies comparable with other popular quantitative chemometric neural network methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Multimode process monitoring based on Bayesian method

Multimode process monitoring has recently attracted much attention both in academy and industry. Conventional methods assume that either the process data are Gaussian in each operation mode, or some process knowledge should be incorporated, thus making the methods supervised. In this paper, a new unsupervised method is developed for multimode process monitoring, which is based on Bayesian inference and two‐step independent component analysis–principal component analysis (ICA–PCA) feature extraction strategy. ICA–PCA is first introduced for feature extraction and dimension reduction. By transferring the traditional monitoring statistic to fault probability in each operation mode, monitoring results in different operation modes can be easily combined by the Bayesian inference. Another contribution of the present paper is the development of a new fault identification method. Through analyses of the posterior probability and the joint probability for the monitored data sample, the correct operation mode or fault scenario can be identified. Three case studies are demonstrated to evaluate the feasibility and efficiency of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

独立成分分析结合在线红外技术研究3,4-双(4'-氨基呋咱基-3')氧化呋咱的合成反应机理

利用在线红外技术监测3,4-双(4'-氨基呋咱基-3')氧化呋咱(DATF)的合成过程,并结合核独立成分分析算法对反应过程中获得的实时红外光谱数据进行解析,得到了反应物、中间体及产物各组分纯物质的红外光谱图.采用密度泛函理论B3LYP法,在6-31+G(d,p)基组水平上求得中间体的红外振动光谱,验证了所分离红外光谱图的正确性,从而推导出合理的合成反应机理.结果表明,核独立成分分析算法能合理地解析红外光谱在线数据,并有效捕捉合成反应的中间体,对合成反应机理的研究具有重要的指导意义.     

Determination of rice type by 1H NMR spectroscopy in combination with different chemometric tools

A 400‐MHz ¹H nuclear magnetic resonance (NMR) spectroscopy and multivariate data analysis were used in the context of food surveillance to discriminate 46 authentic rice samples according to type. It was found that the optimal sample preparation consists of preparing aqueous rice extracts at pH 1.9. For the first time, the chemometric method independent component analysis (ICA) was applied to differentiate clusters of rice from the same type (Basmati, non‐Basmati long‐grain rice, and round‐grain rice) and, to a certain extent, their geographical origin. ICA was found to be superior to classical principal component analysis (PCA) regarding the verification of rice authenticity. The chemical shifts of the principal saccharides and acetic acid were found to be mostly responsible for the observed clustering. Among classification methods (linear discriminant analysis, factorial discriminant analysis, partial least squares discriminant analysis (PLS‐DA), soft independent modeling of class analogy, and ICA), PLS‐DA and ICA gave the best values of specificity (0.96 for both methods) and sensitivity (0.94 for PLS‐DA and 1.0 for ICA). Hence, NMR spectroscopy combined with chemometrics could be used as a screening method in the official control of rice samples. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimation of source infrared spectra profiles of acetylspiramycin active components from troches using kernel independent component analysis

Kernel independent component analysis (KICA), a kind of independent component analysis (ICA) algorithms based on kernel, was preliminarily investigated for blind source separation (BSS) of source spectra profiles from troches. The robustness of different ICA algorithms (KICA, FastICA and Infomax) was first checked by using them in the retrieval of source infrared (IR), ultraviolet (UV) and mass spectra (MS) from synthetic mixtures. It was found that KICA is the most robust method for retrieval of source spectra profiles. KICA algorithm is subsequently adopted in the analysis of diffuse reflection IR of acetylspiramycin (ASPM) troches. It is observed that KICA is able to isolate the theoretically predicted spectral features corresponding to the ASPM active components, excipients and other minor components as different independent (spectral) component. A troche can be authenticated and semi-quantified using the estimated ICs. KICA is an useful method for estimation of source spectral features of molecules with different geometry and stoichiometry, while features belonging to very similar molecules remain grouped.     

Variable selection in visible/near infrared spectra for linear and nonlinear calibrations: A case study to determine soluble solids content of beer

Three effective wavelength (EW) selection methods combined with visible/near infrared (Vis/NIR) spectroscopy were investigated to determine the soluble solids content (SSC) of beer, including successive projections algorithm (SPA), regression coefficient analysis (RCA) and independent component analysis (ICA). A total of 360 samples were prepared for the calibration (n = 180), validation (n = 90) and prediction (n = 90) sets. The performance of different preprocessing was compared. Three calibrations using EWs selected by SPA, RCA and ICA were developed, including linear regression of partial least squares analysis (PLS) and multiple linear regression (MLR), and nonlinear regression of least squares-support vector machine (LS-SVM). Ten EWs selected by SPA achieved the optimal linear SPA-MLR model compared with SPA-PLS, RCA-MLR, RCA-PLS, ICA-MLR and ICA-PLS. The correlation coefficient (r) and root mean square error of prediction (RMSEP) by SPA-MLR were 0.9762 and 0.1808, respectively. Moreover, the newly proposed SPA-LS-SVM model obtained almost the same excellent performance with RCA-LS-SVM and ICA-LS-SVM models, and the r value and RMSEP were 0.9818 and 0.1628, respectively. The nonlinear model SPA-LS-SVM outperformed SPA-MLR model. The overall results indicated that SPA was a powerful way for the selection of EWs, and Vis/NIR spectroscopy incorporated to SPA-LS-SVM was successful for the accurate determination of SSC of beer.     

Uncommon multivariate statistical methods for environmental studies: A review

In this paper we describe the characteristics and the applications of the multivariate methods for spectroscopic and chromatographic techniques independent component analysis (ICA) and two-dimensional correlation spectroscopy (2DCOS) focused to their use in environmental studies. In our opinion, these methods are important because they allow to characterize environmental samples with different aims and scopes from those generally obtained by means of more common multivariate methods such as principal component analysis (PCA) and partial least squares (PLS). The new insights of these methods in recent environmental studies are reviewed and debated.     

Chemometrics-assisted spectrophotometric method for simultaneous determination of vitamins in complex mixtures

An advanced independent component analysis algorithm (MILCA) is applied for simultaneous chemometric determination of fat- and water-soluble vitamins in complex mixtures. The analysis is based on the decomposition of spectra of multicomponent mixtures in the UV region. The key features of the proposed method are simplicity, accuracy, and reliability. Comparisons between the new algorithm and other established methods (MCR-ALS, SIMPLISMA, other ICA techniques) were made. Our results indicate that in most cases, MILCA is comparable or even outperforms other chemometrics methods taken for comparisons. The influence of different factors (abundance of components, noise, step of spectral scan, and scan speed) on decomposition performance has been investigated. The optimal conditions for spectroscopic registration have been identified. The proposed method was used for analysis of model mixtures and real objects (multivitamin drugs, food additives, and energy drinks). The resolved concentrations match well with the declared amounts and the results of reference methods.     

A new statistical method for the automated detection of peaks in UV-DAD chromatograms of a sample mixture

One of the major issues within the context of the fully automated development of chromatographic methods consists of the automated detection and identification of peaks coming from complex samples such as multi-component pharmaceutical formulations or stability studies of these formulations. The same problem can also occur with plant materials or biological matrices. This step is thus critical and time-consuming, especially when a Design of Experiments (DOE) approach is used to generate chromatograms. The use of DOE will often maximize the changes of the analytical conditions in order to explore an experimental domain. Unfortunately, this generally provides very different and “unpredictable” chromatograms which can be difficult to interpret, thus complicating peak detection and peak tracking (i.e. matching peaks among all the chromatograms). In this context, Independent Components Analysis (ICA), a new statistically based signal processing methods was investigated to solve this problem. The ICA principle assumes that the observed signal is the resultant of several phenomena (known as sources) and that all these sources are statistically independent. Under those assumptions, ICA is able to recover the sources which will have a high probability of representing the constitutive components of a chromatogram. In the present study, ICA was successfully applied for the first time to HPLC–UV-DAD chromatograms and it was shown that ICA allows differentiation of noise and artifact components from those of interest by applying clustering methods based on high-order statistics computed on these components. Furthermore, on the basis of the described numerical strategy, it was also possible to reconstruct a cleaned chromatogram with minimum influence of noise and baseline artifacts. This can present a significant advance towards the objective of providing helpful tools for the automated development of liquid chromatography (LC) methods. It seems that analytical investigations could be shortened when using this type of methodologies.