三线性直接分解法分析高维灰色体系

对于由多个两维测量数据组成的三维阵，本文提出一种新三线性直接分解方法。采用高维ＰＣＡ分解，从三维阵中直接提取抽象光谱和抽象浓度，再结合ＱＺ算法，唯一地确定混合物中各组分光谱的浓度。该方法可以排除其它未知组分的干扰，适用于高维灰色体系定性定量分析和多点校准。用模拟数据讨论了光谱分离度对该方法的影响，应用于混合维生素Ｂ１、Ｂ２和Ｂ６的荧光分析，求得的光谱和浓度与实验值吻合很好。     

三维荧光校正法直接测定尿液中的利血平

利用化学计量学三维数据校正方法中的交替三线性分解算法(ATLD)和自加权交替三线性分解算法(SWATLD), 不经化学分离, 对采用激发-发射矩阵荧光法所得到的三维响应数据阵进行三线性成分分解, 再基于标样已知浓度, 利用简单回归法直接测定尿液中利血平(Reserpine)的含量. 结果表明, 当体系的主要组分数取3时, 两种方法均可迅速、 快捷地得到待测物的浓度, 有效地解决了荧光法定量测定时未知背景及干扰物光谱严重重叠而引起的问题.     

三线性分解方法用于光谱数据中背景漂移的扣除

在光谱测量中, 通常会发生光谱背景漂移现象. 引起光谱背景漂移的因素有很多, 如仪器的背景噪声变化, 测量时环境温度的变化, 光源如氙灯的使用时间等等. 针对三维光谱数阵, 发展了一种基于交替三线性分解(ATLD)算法的化学计量学方法用来处理光谱背景漂移问题. 该方法在进行三线性分解时, 对待光谱背景漂移与感兴趣组分一样, 将其单独当作一个组分或因子来考虑, 并将其从分解得到的相应矩阵中提取出来, 构建一个光谱背景漂移阵, 然后从三维原始响应数阵中将其减掉, 从而达到成功扣除光谱背景漂移的目的. 采用发展的方法处理2组模拟数据和2组实验数据, 都获得了满意的结果. 另外, 对于非线性较严重的背景漂移, 通过再进行一次扣除, 即“二次扣除”, 也达到了理想的效果. 该方法有望发展成为一种很有潜力的光谱预处理技术.     

多维数据解析联用三维荧光光谱检测污水中酚类污染物残留

应用三维荧光结合化学计量学中的二阶校正方法对城市污水中的苯酚、对苯二酚和邻苯二酚进行了定量分析研究.选用β-环糊精作为荧光增敏剂,三维荧光激发波长范围205～450 nm,发射波长范围215～320 nm.通过自加权交替三线性分解(SWATLD)解析得到的苯酚的平均回收率为95.84±0.41％,对苯二酚的平均回收率为102.31±0.44％,邻苯二酚的平均回收率为100.27±0.43％.该方法前处理简单,不需预先分离,可以快速定量分析污水中光谱相互干扰的多个待测组分的含量.     

应用二阶校正算法-荧光分光光度法同时测定血浆中诺氟沙星和左氧氟沙星

应用三维荧光技术,结合化学计量学中的二阶校正算法,在诺氟沙星和左氧氟沙星荧光光谱严重重叠,以及干扰物质存在下对血浆中两种喹诺酮类药物进行了同时定量分析。三维荧光激发波长范围265～510nm,发射波长范围300～650 nm。交替不对称三线性分解(AATLD)算法解析得到的诺氟沙星和左氧氟沙星的平均回收率分别为96.9%和103.9%。方法前处理简单、不需预先分离、可以快速定量分析血浆中光谱相互干扰的待测药物的含量。     

三维荧光光谱结合二阶校正算法用于尿液中常见毒品的检测

利用三维荧光光谱技术结合二阶校正算法对尿液中冰毒、3,4-亚甲基二氧基甲基苯丙胺、可卡因和吗啡4种毒品进行快速定量分析.结果表明,平行因子(PARAFAC)、交替三线性分解(ATLD)和自加权交替三线性分解(SWATLD)算法均能很好地分辨出待测组分,且通过PARAFAC与SWATLD算法解析三维光谱数据获得的尿液背景干扰下4种毒品的平均回收率为92.8%~106.1%,相对误差低于8%.三维荧光光谱结合二阶校正算法可用于常见毒品滥用者的快速检测,为缉毒禁毒工作提供新的检测手段.     

三维荧光二阶校正方法用于体液和细胞培养基中五味子甲素含量的快速测定

采用三维激发发射荧光光谱结合自加权交替三线性分解(SWATLD)二阶校正方法, 对人体液样(血浆样及尿液样)和细胞培养基样中五味子甲素的含量进行了直接快速定量分析. 在血浆背景、尿液背景和细胞培养基背景共存下, 当分析体系的组分数分别选择2时, 用SWATLD二阶校正方法获得相应五味子甲素的平均回收率分别为(100.4±1.6)%, (100.5±6.3)%和(103.6±4.5)%. 实验结果表明, 此方法不仅能够较好地解决这些复杂分析体系因背景内源荧光性物质与待分析物光谱严重重叠所引起的难分辨的问题, 还可以用于直接快速准确定量分析.     

三维荧光二阶校正法用于未知混合物中苯酚含量的测定

将三维荧光光谱技术与秩消失因子分析、广义秩消失因子分析和交替三线性分解3种二阶校正方法相结合,建立了测定未知混合物中苯酚含量的三维荧光二阶校正新方法。设定在激发波长240~280 nm和发射波长280~360 nm范围内测定未知混合物中苯酚的三维荧光光谱,构建三维响应数据阵,运用基于三线性分解的二阶校正算法进行解析。结果表明,当模拟样品的组分数为2时,秩消失因子分析、广义秩消失因子分析和交替三线性分解3种方法测定苯酚的预测均方根误差分别为0.33,1.18和0.15,平均回收率分别为101.6%,115.6%和101.9%;当组分数为3时,3种方法的预测均方根误差则分别为1.61,1.80和0.51,平均回收率分别为134.2%,133.9%和107.1%;将其分别应用于实际样品中苯酚的测定,结果满意,且交替三线性分解法的测定结果优于秩消失因子分析法和广义秩消失因子分析法。     

三维荧光二阶校正法快速测定人尿样中奥沙普秦含量

利用三维荧光光谱技术,结合分别基于自加权交替三线性分解(SWATLD)和交替归一加权残差(ANWE)算法的二阶校正方法,直接快速测定人体样液中以及萘丁美酮或萘普生于扰共存下奥沙普秦的含量.利用本方法的"二阶优势",在尿液内源物质及萘丁美酮或萘普生干扰共存下有效地分辨出奥沙普秦的激发发射荧光光谱.采用SWATLD和ANW...     

三维荧光二阶校正法用于尿液样中氢化可的松的定量测定

本文提出了三维荧光光谱结合二阶校正算法实现人体尿液样中氢化可的松定量测定的新方法。氢化可的松本身的荧光较弱,但与浓硫酸反应后可以生成强荧光的化合物。利用这一特性,采用浓硫酸为氧化剂,设定在激发波长为300-370nm、发射波长为400-580nm范围内测定尿液样中氢化可的松的三维荧光光谱,构建三维响应数据阵,然后运用基于三线性分解的二阶校正算法进行解析。当组分数N取3时,采用基于平行因子分析（PARAFAC）算法的Z-阶校正法的平均回收率为98.6±4.1％,预测残差平方根（RMSEP）为0.0114;采用基于满秩平行因子分析（FRA-PARAFAc）算法的二阶校正法的平均回收率和RMSEP分别为99.3±2.4％和0.0066。两种算法可以得到相近且满意的结果。     

A flexible trilinear decomposition algorithm for three-way calibration based on the trilinear component model and a theoretical extension of the algorithm to the multilinear component model

There is a great deal of interest in decompositions of multilinear component models in the field of multi-way calibration, especially the three-way case. A flexible novel trilinear decomposition algorithm of the trilinear component model as a modification of an alternating least squares algorithm for three-way calibration is proposed. The proposed algorithm (constrained alternating trilinear decomposition, CATLD) is based on an alternating approximate least-squares scheme, in which two extra terms are added to each loss function, making it more efficient and flexible. The analysis of simulated three-way data arrays shows that it converges fast, is insensitive to initialization, and is insensitive to the overestimated number of components used in the decomposition. The analysis of real excitation–emission matrix (EEM) fluorescence and real high performance liquid chromatography–photodiode array detection (HPLC–DAD) data arrays confirms the results of the simulation studies, and shows that the proposed algorithm is favorable not only for EEMs but also for HPLC–DAD data. The three-way calibration method based on the CATLD algorithm is very efficient and flexible for direct quantitative analysis of multiple analytes of interest in complex systems, even in the presence of uncalibrated interferents and varying background interferents. Additionally, a theoretical extension of the proposed algorithm to the multilinear component model (constrained alternating multilinear decomposition, CAMLD) is developed.     

Estimating the chemical rank of three-way data arrays by a simple linear transform incorporating Monte Carlo simulation

Estimating an appropriate chemical rank of a three-way data array is very important to second-order calibration. In this paper, a simple linear transform incorporating Monte Carlo simulation approach (LTMC) to estimate the chemical rank of a three-way data array was suggested. The new method determines the chemical rank through performing a simple linear transform procedure on the original cube matrix to produce two subspaces by singular value decomposition. One of two subspaces is derived from the original three-way data array itself and the other is derived from a new three-way data array produced by the linear transformation of the original one. Projection technique incorporating the Monte Carlo approach acts as distinguishing criterion to choose the appropriate component number of the system. Simulated three-way trilinear data arrays with different noise types (homoscedastic and heteroscedastic), various noise level as well as high collinearity are used to illustrate the feasibility of the new method. The results have shown that the new method could yield accurate results with different conditions appended. The feasibility of the new method is also confirmed by two real arrays, HPLC-DAD data and excitation-emission fluorescent data. All the results are compared with the other three factor-determining methods: factor indicator function (IND), core consistency diagnostic (CORCONDIA) and two-mode subspace comparison (TMSC) approach. It shows that the newly proposed algorithm can objectively and quickly determine the chemical rank to fit the trilinear model.     

Use of pseudo-sample extraction and the projection technique to estimate the chemical rank of three-way data arrays

Determining the rank of a trilinear data array is a first step in subsequent trilinear component decomposition. Different from estimating the rank of bilinear data, it is more difficult to decide the significant number of component to fit the trilinear decompositions exactly. General methods of rank estimation utilize the information contained in the singular values but ignore information from eigenvectors. In this paper, a rank estimating method specifically for trilinear data arrays is proposed. It uses the idea of direct trilinear decomposition (DTLD) to compress the cube matrix into two pseudo sample matrices which are then decomposed by singular value decomposition. Two eigenvectors combined with the projection technique are used to estimate the rank of trilinear data arrays. Simulated trilinear data arrays with homoscedastic and heteroscedastic noise, different noise levels, high collinearity, and real three-way data arrays have been used to illustrate the feasibility of the proposed method. Compared with other factor-determining methods, for example use of the factor indication function (IND), residual percentage variance (RPV), and the two-mode subspace comparison approach (TMSC), the results showed that the new method can give more reliable answers under the different conditions applied.      

三线性分解算法对液相色谱-质谱联用仪多样本测定数据分辨适用性的比较

从三线性分解算法对液相色谱-质谱联用仪(LC-MS)多样本测定数据分辨的适用性角度入手,探讨了双线性和三线性分解算法的实际应用效果、存在的问题及其解决方案。本文选择含有低丰度肽段和高干扰背景信号的代表性测定数据进行测试。结果表明,双线性方法不具有分辨唯一性,不能分离LC-MS多样品测定数据存在的背景干扰,从而不适用于低丰度肽段问题的分析。常规的三线性分解算法难以满足质谱信号具有的数学特性--稀疏性,分辨结果并不完全可靠。本文提出了具有非负约束的交替三线性分解(non-negative alternating trilinear decomposition, NNATLD)新算法用于LC-MS多样本测定数据分辨及数学分离,能够很好地适应质谱的数学特性,且具有计算资源节约和收敛速度快等特点。     

Algorithm combination strategy to obtain the second‐order advantage: simultaneous determination of target analytes in plasma using three‐dimensional fluorescence spectroscopy

Although a number of algorithms have established to obtain the well‐known second‐order advantage that quantifies analytes of interest in the presence of interferents, each has associated problems. In this work, for the first time, the optimization procedure of trilinear decomposition has been divided into three subparts, and a novel strategy is developed for assembling the advantages of the alternating trilinear decomposition (ATLD) algorithm, the self‐weighted alternating trilinear decomposition (SWATLD) algorithm, and the parallel factor analysis (PARAFAC) algorithm. The performance of the proposed strategy was evaluated using a simulated data set, a published fluorescence data set together with a new fluorescence data set that simultaneously quantifies procaine and tetracaine in plasma. Results show that the novel method can accurately and effectively estimate the qualitative and quantitative information of analytes of interest. Besides, the resolved profiles are very stable with respect to the number of components as long as the employed number is chosen to be equal or larger than the underlying one. Additionally, the study confirms that better prediction can be obtained by the new strategy when compared with ATLD, SWATLD, and PARAFAC as well as the strategy that employs direct trilinear decomposition method as initial values for PARAFAC. Moreover, the strategy can be directly extended to third‐order or higher‐order data analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Mitigating model deficiency in three-way data analysis by the combination of background constraining and iterative correcting techniques

PARAFAC is a popular model for trilinear data analysis in analytical chemistry. The prerequisite for the successful application of PARAFAC in analytical chemistry is that the three-way data array should follow a trilinear model, which is always violated by the presence of deviations such as Rayleigh scattering in fluorescence spectroscopy. In order to mitigate the influence of model deviations, background constraining and iterative correcting techniques are advocated in this contribution. The method established on these two techniques can nearly eliminate the effect of model deviation on the chemical loading parameters estimated. Compared with other methods for mitigating model deviations, the proposed method requires no prior knowledge about the chemical loading parameters. It is also unnecessary to assign weights to data entities as the weighted PARAFAC of Anderson does. Its implementation is comparable to PARAFAC-ALS and can be programmed to be completely automatic. Its performance has been demonstrated by fluorescent and chromatographic experiments.     

Analytical solution and meaning of feasible regions in two-component three-way arrays

Although many efforts have been directed to the development of approximation methods for determining the extent of feasible regions in two- and three-way data sets; analytical determination (i.e. using only finite-step direct calculation(s) instead of the less exact numerical ones) of feasible regions in three-way arrays has remained unexplored. In this contribution, an analytical solution of trilinear decomposition is introduced which can be considered as a new direct method for the resolution of three-way two-component systems. The proposed analytical calculation method is applied to the full rank three-way data array and arrays with rank overlap (a type of rank deficiency) loadings in a mode. Close inspections of the analytically calculated feasible regions of rank deficient cases help us to make clearer the information gathered from multi-way problems frequently emerged in physics, chemistry, biology, agricultural, environmental and clinical sciences, etc. These examinations can also help to answer, e.g., the following practical question: “Is two-component three-way data with proportional loading in a mode actually a three-way data array?” By the aid of the additional information resulted from the investigated feasible regions of two-component three-way data arrays with proportional profile in a mode, reasons for the inadequacy of the seemingly trilinear data treatment methods published in the literature (e.g., U-PLS/RBL-LD that was used for extraction of quantitative and qualitative information reported by Olivieri et al. (Anal. Chem. 82 (2010) 4510–4519)) could be completely understood.     

Trilinear decomposition method applied to removal of three-dimensional background drift in comprehensive two-dimensional separation data

A novel technique for removal of three-dimensional background drift in comprehensive two-dimensional (2D) liquid chromatography coupled with diode array detection (LCxLC-DAD) data is proposed. The basic idea is to perform trilinear decomposition on the instrumental response data, which is based on the alternating trilinear decomposition (ATLD) algorithm. In model construction, the background drift is modeled as one component or factor as well as the analytes of interest, hence, the drift is explicitly included into the calibration. The method involves performing trilinear decomposition on the raw data, then extracting the background component and subtracting this background data from the raw data, leaving the analytes' signal on a flat baseline. Simultaneous evaluation of three-dimensional background drift and true signals may improve the quality of the data. This method is applied to the determination and removal of three-dimensional background drifts in simulated multidimensional data as well as experimental comprehensive two-dimensional liquid chromatographic data. It is shown that this technique yield a good removal of background drift, without the need to perform a blank chromatographic run, and required no prior knowledge about the sample composition.     

A novel efficient way to estimate the chemical rank of high-way data arrays

A novel method, a subspace projection of pseudo high-way data array (SPPH), was developed for estimating the chemical rank of high-way data arrays. The proposed method determines the chemical rank through performing singular value decomposition (SVD) on the slice matrices of original high-way data array to produce a pseudo high-way data array and employing the idea of the difference of the original truncated data set and the pseudo one. Compared with traditional methods, it uses the information from eigenvectors combined with the projection residual to estimate the rank of the three-way data arrays instead of using the eigenvalue. In order to demonstrate the excellent performance of the new method, simulated and real three-way data arrays were carried out by the proposed method. The results showed that the proposed method could accurately and quickly determine the chemical rank to fit the trilinear model. Moreover, the newly proposed method was compared with the other four factor-determining methods, i.e. factor indicator function (IND), ADD-ONE-UP, core consistency diagnostic (CORCONDIA) and two-mode subspace comparison (TMSC) approaches. It was found that the proposed method can deal with more complex situations with existence of severe collinearity and trace concentration than many other methods can and performs well in practical applications.