多元校正新算法研究和二维数据分析方法在色谱分离评价中的应用
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摘要
本文作者对多元校正中的一些难点问题进行了深入的研究,提出了多种新型化学计量学算法,并将其应用于标准校正数据集的研究,另外也对化学计量学二维数据分析方法在色谱分离质量评价中的应用进行了一些研究。本论文主要包括以下几个方面的工作:
1.探讨了多元校正建模中的训练集样品的代表性和最优化样品加权问题。由于多元校正的样品光谱空间的多维性和复杂性以及样品选取过程中的不确定性,准确估计训练集样品在整个样品空间的代表性尚存在一定困难。传统的多元校正模型大多根据经验方法选择代表性样品,在某些不利的情况下可能会影响校正模型对新样品的预测性能。为解决以上问题,同时考虑到样品的代表性很难通过考察单个样品进行估计,我们把全局优化样品加权的思想和偏最小二乘相结合,提出了最优化样品加权偏最小二乘这一新算法。该算法通过对原来的训练集样品进行非负加权,在校正建模过程中同时考虑了模型的复杂性和预测能力,最优样品权重通过粒子群优化算法搜索获得。另外,为了使样品加权偏最小二乘的建模和优化更加易于计算,我们进一步证明了样品加权校正模型可通过对每个样品的光谱数据和组分浓度值乘以一个相同的非负常数实现。将该算法应用于真实的标准数据集的结果表明,在原始校正样品的代表性较差时,最优化样品加权偏最小二乘算法确实能够改善模型的预测性能。
2.基于粒子群优化算法,我们提出了一种较传统的变量选择方法更为灵活的变量加权方法。通过对传统的基于变量选择的校正模型的考察可以发现,进入校正模型的变量实际上被赋予权重1,而被模型舍弃的变量的权重实则为0。如果把权重的概念引入变量选择,允许变量的权重取非负的连续值,则传统的变量选择只是变量加权的一种特殊情况。另外,由于变量加权的目标是同时优化校正集的训练和验证集的预测,连续非负的变量加权实际上可视为对光谱变量的某种最优化重新刻度,因此比传统的变量选择有更多的灵活性。对真实校正数据集的研究表明,变量加权偏最小二乘方法不仅能起到变量选择的作用,还能够在校正模型中保留较多的变量,保持了多元校正的多通道优势。
3.我们改进了一种新的机器学习算法—叠加回归,并将其应用于多元校正,同时实现了波长区间的快速自动优化选择和校正模型组合。我们用蒙特卡罗交互验证代替了叠加回归中的传统的交互验证,再用改进了的叠加回归算法组合建立在单个波长子区间上的偏最小二乘模型,所得模型在组合系数非负的约束下具有最小的蒙特卡罗交互验证均方根误差,所以可以期望组合模型具有较好的泛化性能和防止过拟合的能力。叠加回归能够通过非负最小二乘法确定模型组合系数,把某些光谱子区间模型对应的组合系数置为0,从而实现波长子区间的自动选择。另外,由于线性组合模型的蒙特卡罗交互验证可通过组合一系列子模型的蒙特卡罗交互验证来实现,而单个的光谱子区间模型的交互验证计算量很小,所以该方法与同类区间选择方法相比,计算量要小得多。对标准校正数据集的研究进一步证实了该方法的实用性。
4.我们提出了一种多元校正中近红外光谱数据预处理的新概念—群预处理方法。由于近红外光谱数据经常受到背景、基线漂移和噪声等不利因素的影响,对原始光谱测量数据进行适当的预处理在很多情况下已经成为多元校正的必要步骤。但是,由于光谱的复杂性和先验信息的缺乏,确定最好的预处理方法常常需要多次尝试,并且要求操作者有一定的数据处理经验;另外,单一的预处理方法在改善数据的某些方面的同时,也可能带来某些方面的负面影响和面临信息丢失的风险,并且基于单一预处理方法的校正模型对新样品的预测可能缺乏稳定性。为解决以上问题,我们提出了近红外光谱的群预处理方法,该方法用蒙特卡罗交互验证叠加回归算法组合一系列基于不同预处理方法的校正模型,可以实现预处理方法的自动选择和优化加权。对真实校正数据集的研究结果表明,基于群预处理方法的校正模型与基于单一预处理方法的校正模型相比,不仅保持或改善了原有模型的准确性,而且模型的稳定性有所提高。
5.我们把移动窗口偏最小二乘算法应用于多元校正的模型转移,建立了高稳定性和低复杂度的全局校正模型。当把已有的校正模型应用于新样品的光谱校正时,如果新样品的光谱含有与模型的训练样品不相同的光谱贡献时,为防止出现偏差和严重的误差,就需要对原有的校正模型进行校正转移。我们把一种新的波长区间选择方法—移动窗口偏最小二乘法引入到全局校正模型中。移动窗口偏最小二乘法能够选择与化学组分相关的光谱子区间,并且能够降低全局模型的复杂度。通过对标准的校正数据集的研究,基于移动窗口偏最小二乘的全局模型确实体现了上述优点,较好地实现了校正模型的转移。
6.我们讨论了基于单通道检测器的色谱图的传统的色谱分离标准在估计色谱分离质量时可能遇到的问题,并且指出,很多问题都是由于一维色谱图在严重峰重叠的情况下缺少诸如组分数、重叠度和峰纯度等信息造成的。然后,我们综述了化学计量学二维数据分析方法在色谱分离效率评价中的应用,并且依据文献和我们的研究经验,对某些重要问题进行了讨论。7.我们提出了一种新的基于秩图的色谱分离评价指标—峰纯度加权分辨率。与传统的基于单通道信号检测器的色谱分离标准相比,峰纯度加权分辨率的优势在于它同时利用了化学组分数、重叠程度、流出时间和峰纯度等关键色谱信息,而这些信息在色谱峰严重重叠时是很难从一维色谱信号中获得的。对模拟色谱体系和一个真实色谱体系的研究表明,峰纯度加权分辨率的值能合理地反映色谱重叠程度的大小,该标准确实可用于严重重叠的色谱图的分离估计。最后,我们还讨论了使用峰纯度加权分辨率时应当注意的问题。
The research work in this thesis focuses on new chemometric algoritms for multivariate calibration and the applications of two-way data analysis methods to chromatographic separation evaluation.
The representiveness of training samples for multivariate calibration has been discussed and the concept of weighted sampling has been introduced to multivariate calibration. Due to the high-dimensionality and complexity of spectral data space and the uncertainty involved in sampling process, the representiveness of training samples in the whole smple space is difficult to evaluate and selection of representative training samples for multivariate calibration depends largely on experiential methods. If the training samples fail to represent the sample space, sometimes the predictions of new samples can be degraded. In order to solve this problem, a new algorithm for multivariate calibration is developed by combining optimized sampling and partial least squares (PLS), where the original training samples are non-negatively weighted and the complexity and predictivity of the model are considered simutaneously. Moreover, it has been proved that weighted sampling can be achieved by multiplying both the spectrum and concentration value of a sample by the same non-negative constant, which has made the computation of sample-weighted models much easier. Two real data sets are investigated and the results demonstrate that sample-weighted PLS models can improve the predictivity of a model when the representiveness of original calibration sample is poor.
Based on particle swarm optimization (PSO) algorithm, a more flexible method for variable selection, variable weighting is proposed. We have revisited traditional variable selection methods and found that in such methods the variables included in the model are essentially weighted with ones and those excluded from the model are weighted with zeros. If continuous non-negative weights are allowed, the traditional variable selection is just a special case of variable weighting. Since the variable weights are determined to simultaneously optimize the training of calibration set and the prediction of validation set, variable weighting can be seen as an optimized rescaling of the variables in certain sense and therefore is more flexible than traditional variable selection methods. Results obtained from real data sets indicate that variable-weighted PLS (VW-PLS) can not only play the same role as variable selection but can also maintain the multi-channel advantage by including more variables in the model.
A new machine learning method, stacked regression is improved and then introduced to multivariate calibration to achieve automatic and fast sepectral interval selection. Instead of traditional cross validation (CV), Monte Carlo cross validation (MCCV) is adopted in the improved stacked regression, which is then used to combine the regression models built on different spectral intervals. With the non-negative constraints of the cobination coefficients, the resulted combined model has the minimum root mean squared error of MCCV (RMSEMCCV), so the model is expected to have good generalizing ability and less risk of overfitting. Stacked regression can obtain the combination coefficients by non-negative least squares (NNLS) and spectral interval selection is achieved by setting some coefficients to be zeros. Moreover, because MCCV of a linearly combined model can be achieved by linearly combining the MCCV of the separate interval models, which is much simpler to compute, the computation of MCCV stacked regression is economical. The practicability of the proposed method is demonstrated by its applications to two real data sets.
A new concept of data preprocessing for multivariate calibration, ensemble preprocessing is proposed. Because the raw near infrared (NIR) spectra are often influenced by factors such as backgrounds, baseline shifts and noise, it is necessary to preprocess the raw data properly in multivariate calibration. However, due to the complexity of NIR data and lack of prior information, to achieve the optimal data preprocessing is still trial and error and requires the experience of practitoners. Another disadvantage of traditional preprocessing methods is that any preprocessing method has the risk of information loss and might degrade the data in some aspects while improving the data in certain aspects. Moreover, models based on a single preprocessing method are sometimes instable for predicting new samples. To solve the above problems and achieve the automatic selection and optimization of preprocessing methods, an ensemble preprocessing method is developed by combining calibration models based on different preprocessing methods through MCCV stacked regression. Results obtained from real data sets demonstrate that compared with traditional preprocessing using a single method, ensemple preprocessing can lead to a more stable calibration model while maintaining or improving the precision of the model.
Moving window partial least squares regression (MWPLSR) is introduced to calibration transfer to develop a stable and low-complexity global calibration model. When applied to new samples containing spectral variations not calibrated, the existing calibration model should be adjusted to avoid bias and serious error. MWPLSR can select concentration-correlated spectral intervals and reduce the complexity of the global calibration model. Investigation of two benchmark data sets has confirmed that global calibration model based on MWPLSR has the above advandages as expected and can achieve stable and reliable calibration transfer.
The disadvantages of traditional chromatographic separation criteria based on chromatograms recorded by single-channel detectors are discussed. It is further pointed out that many of these problems are caused by lack of information concerning number of components, peak purity and overlap degree in the presence of seriously overlapped peaks. Then the applications of two-way chemometric methods to assessing chromatographic separation quality are reviewed and some important problems involved are discussed according to literatures and our research experience.
A new chromatographic separation criterion, peak-purity weighted resolution (PPWR) based on rank graph is proposed. Compared with traditional separation criteria based on one-way chromatograms, the advantages of PPWR lie in the fact that it gracefully considers the information concerning number of components, peak purity and overlap degree, which is difficult to obtain from one-way chromatograms with serious overlaps. PPWR is applied to a simulated data set and a real chromatograhic system, indicating PPWR is indeed a reasonable separation criterion for seriously overlapped peaks and can reflect the overlap degree. Finally some important problems that might be encounted when using PPWR are discussed.
1.探讨了多元校正建模中的训练集样品的代表性和最优化样品加权问题。由于多元校正的样品光谱空间的多维性和复杂性以及样品选取过程中的不确定性,准确估计训练集样品在整个样品空间的代表性尚存在一定困难。传统的多元校正模型大多根据经验方法选择代表性样品,在某些不利的情况下可能会影响校正模型对新样品的预测性能。为解决以上问题,同时考虑到样品的代表性很难通过考察单个样品进行估计,我们把全局优化样品加权的思想和偏最小二乘相结合,提出了最优化样品加权偏最小二乘这一新算法。该算法通过对原来的训练集样品进行非负加权,在校正建模过程中同时考虑了模型的复杂性和预测能力,最优样品权重通过粒子群优化算法搜索获得。另外,为了使样品加权偏最小二乘的建模和优化更加易于计算,我们进一步证明了样品加权校正模型可通过对每个样品的光谱数据和组分浓度值乘以一个相同的非负常数实现。将该算法应用于真实的标准数据集的结果表明,在原始校正样品的代表性较差时,最优化样品加权偏最小二乘算法确实能够改善模型的预测性能。
2.基于粒子群优化算法,我们提出了一种较传统的变量选择方法更为灵活的变量加权方法。通过对传统的基于变量选择的校正模型的考察可以发现,进入校正模型的变量实际上被赋予权重1,而被模型舍弃的变量的权重实则为0。如果把权重的概念引入变量选择,允许变量的权重取非负的连续值,则传统的变量选择只是变量加权的一种特殊情况。另外,由于变量加权的目标是同时优化校正集的训练和验证集的预测,连续非负的变量加权实际上可视为对光谱变量的某种最优化重新刻度,因此比传统的变量选择有更多的灵活性。对真实校正数据集的研究表明,变量加权偏最小二乘方法不仅能起到变量选择的作用,还能够在校正模型中保留较多的变量,保持了多元校正的多通道优势。
3.我们改进了一种新的机器学习算法—叠加回归,并将其应用于多元校正,同时实现了波长区间的快速自动优化选择和校正模型组合。我们用蒙特卡罗交互验证代替了叠加回归中的传统的交互验证,再用改进了的叠加回归算法组合建立在单个波长子区间上的偏最小二乘模型,所得模型在组合系数非负的约束下具有最小的蒙特卡罗交互验证均方根误差,所以可以期望组合模型具有较好的泛化性能和防止过拟合的能力。叠加回归能够通过非负最小二乘法确定模型组合系数,把某些光谱子区间模型对应的组合系数置为0,从而实现波长子区间的自动选择。另外,由于线性组合模型的蒙特卡罗交互验证可通过组合一系列子模型的蒙特卡罗交互验证来实现,而单个的光谱子区间模型的交互验证计算量很小,所以该方法与同类区间选择方法相比,计算量要小得多。对标准校正数据集的研究进一步证实了该方法的实用性。
4.我们提出了一种多元校正中近红外光谱数据预处理的新概念—群预处理方法。由于近红外光谱数据经常受到背景、基线漂移和噪声等不利因素的影响,对原始光谱测量数据进行适当的预处理在很多情况下已经成为多元校正的必要步骤。但是,由于光谱的复杂性和先验信息的缺乏,确定最好的预处理方法常常需要多次尝试,并且要求操作者有一定的数据处理经验;另外,单一的预处理方法在改善数据的某些方面的同时,也可能带来某些方面的负面影响和面临信息丢失的风险,并且基于单一预处理方法的校正模型对新样品的预测可能缺乏稳定性。为解决以上问题,我们提出了近红外光谱的群预处理方法,该方法用蒙特卡罗交互验证叠加回归算法组合一系列基于不同预处理方法的校正模型,可以实现预处理方法的自动选择和优化加权。对真实校正数据集的研究结果表明,基于群预处理方法的校正模型与基于单一预处理方法的校正模型相比,不仅保持或改善了原有模型的准确性,而且模型的稳定性有所提高。
5.我们把移动窗口偏最小二乘算法应用于多元校正的模型转移,建立了高稳定性和低复杂度的全局校正模型。当把已有的校正模型应用于新样品的光谱校正时,如果新样品的光谱含有与模型的训练样品不相同的光谱贡献时,为防止出现偏差和严重的误差,就需要对原有的校正模型进行校正转移。我们把一种新的波长区间选择方法—移动窗口偏最小二乘法引入到全局校正模型中。移动窗口偏最小二乘法能够选择与化学组分相关的光谱子区间,并且能够降低全局模型的复杂度。通过对标准的校正数据集的研究,基于移动窗口偏最小二乘的全局模型确实体现了上述优点,较好地实现了校正模型的转移。
6.我们讨论了基于单通道检测器的色谱图的传统的色谱分离标准在估计色谱分离质量时可能遇到的问题,并且指出,很多问题都是由于一维色谱图在严重峰重叠的情况下缺少诸如组分数、重叠度和峰纯度等信息造成的。然后,我们综述了化学计量学二维数据分析方法在色谱分离效率评价中的应用,并且依据文献和我们的研究经验,对某些重要问题进行了讨论。7.我们提出了一种新的基于秩图的色谱分离评价指标—峰纯度加权分辨率。与传统的基于单通道信号检测器的色谱分离标准相比,峰纯度加权分辨率的优势在于它同时利用了化学组分数、重叠程度、流出时间和峰纯度等关键色谱信息,而这些信息在色谱峰严重重叠时是很难从一维色谱信号中获得的。对模拟色谱体系和一个真实色谱体系的研究表明,峰纯度加权分辨率的值能合理地反映色谱重叠程度的大小,该标准确实可用于严重重叠的色谱图的分离估计。最后,我们还讨论了使用峰纯度加权分辨率时应当注意的问题。
The research work in this thesis focuses on new chemometric algoritms for multivariate calibration and the applications of two-way data analysis methods to chromatographic separation evaluation.
The representiveness of training samples for multivariate calibration has been discussed and the concept of weighted sampling has been introduced to multivariate calibration. Due to the high-dimensionality and complexity of spectral data space and the uncertainty involved in sampling process, the representiveness of training samples in the whole smple space is difficult to evaluate and selection of representative training samples for multivariate calibration depends largely on experiential methods. If the training samples fail to represent the sample space, sometimes the predictions of new samples can be degraded. In order to solve this problem, a new algorithm for multivariate calibration is developed by combining optimized sampling and partial least squares (PLS), where the original training samples are non-negatively weighted and the complexity and predictivity of the model are considered simutaneously. Moreover, it has been proved that weighted sampling can be achieved by multiplying both the spectrum and concentration value of a sample by the same non-negative constant, which has made the computation of sample-weighted models much easier. Two real data sets are investigated and the results demonstrate that sample-weighted PLS models can improve the predictivity of a model when the representiveness of original calibration sample is poor.
Based on particle swarm optimization (PSO) algorithm, a more flexible method for variable selection, variable weighting is proposed. We have revisited traditional variable selection methods and found that in such methods the variables included in the model are essentially weighted with ones and those excluded from the model are weighted with zeros. If continuous non-negative weights are allowed, the traditional variable selection is just a special case of variable weighting. Since the variable weights are determined to simultaneously optimize the training of calibration set and the prediction of validation set, variable weighting can be seen as an optimized rescaling of the variables in certain sense and therefore is more flexible than traditional variable selection methods. Results obtained from real data sets indicate that variable-weighted PLS (VW-PLS) can not only play the same role as variable selection but can also maintain the multi-channel advantage by including more variables in the model.
A new machine learning method, stacked regression is improved and then introduced to multivariate calibration to achieve automatic and fast sepectral interval selection. Instead of traditional cross validation (CV), Monte Carlo cross validation (MCCV) is adopted in the improved stacked regression, which is then used to combine the regression models built on different spectral intervals. With the non-negative constraints of the cobination coefficients, the resulted combined model has the minimum root mean squared error of MCCV (RMSEMCCV), so the model is expected to have good generalizing ability and less risk of overfitting. Stacked regression can obtain the combination coefficients by non-negative least squares (NNLS) and spectral interval selection is achieved by setting some coefficients to be zeros. Moreover, because MCCV of a linearly combined model can be achieved by linearly combining the MCCV of the separate interval models, which is much simpler to compute, the computation of MCCV stacked regression is economical. The practicability of the proposed method is demonstrated by its applications to two real data sets.
A new concept of data preprocessing for multivariate calibration, ensemble preprocessing is proposed. Because the raw near infrared (NIR) spectra are often influenced by factors such as backgrounds, baseline shifts and noise, it is necessary to preprocess the raw data properly in multivariate calibration. However, due to the complexity of NIR data and lack of prior information, to achieve the optimal data preprocessing is still trial and error and requires the experience of practitoners. Another disadvantage of traditional preprocessing methods is that any preprocessing method has the risk of information loss and might degrade the data in some aspects while improving the data in certain aspects. Moreover, models based on a single preprocessing method are sometimes instable for predicting new samples. To solve the above problems and achieve the automatic selection and optimization of preprocessing methods, an ensemble preprocessing method is developed by combining calibration models based on different preprocessing methods through MCCV stacked regression. Results obtained from real data sets demonstrate that compared with traditional preprocessing using a single method, ensemple preprocessing can lead to a more stable calibration model while maintaining or improving the precision of the model.
Moving window partial least squares regression (MWPLSR) is introduced to calibration transfer to develop a stable and low-complexity global calibration model. When applied to new samples containing spectral variations not calibrated, the existing calibration model should be adjusted to avoid bias and serious error. MWPLSR can select concentration-correlated spectral intervals and reduce the complexity of the global calibration model. Investigation of two benchmark data sets has confirmed that global calibration model based on MWPLSR has the above advandages as expected and can achieve stable and reliable calibration transfer.
The disadvantages of traditional chromatographic separation criteria based on chromatograms recorded by single-channel detectors are discussed. It is further pointed out that many of these problems are caused by lack of information concerning number of components, peak purity and overlap degree in the presence of seriously overlapped peaks. Then the applications of two-way chemometric methods to assessing chromatographic separation quality are reviewed and some important problems involved are discussed according to literatures and our research experience.
A new chromatographic separation criterion, peak-purity weighted resolution (PPWR) based on rank graph is proposed. Compared with traditional separation criteria based on one-way chromatograms, the advantages of PPWR lie in the fact that it gracefully considers the information concerning number of components, peak purity and overlap degree, which is difficult to obtain from one-way chromatograms with serious overlaps. PPWR is applied to a simulated data set and a real chromatograhic system, indicating PPWR is indeed a reasonable separation criterion for seriously overlapped peaks and can reflect the overlap degree. Finally some important problems that might be encounted when using PPWR are discussed.
引文
[1]俞汝勤.化学计量学导论.长沙:湖南教育出版社, 1991
[2]高鸿.分析化学前沿.北京:科学出版社, 1991
[3]梁逸曾.白灰黑复杂多组分分析体系及其化学计量学算法.长沙:湖南科技出版社, 1997
[4]陆晓华.化学计量学.武汉:华中理工大学出版社, 1997
[5]梁逸曾,俞汝勤.分析化学手册(第十分册)化学计量学.北京:化工出版社, 2000
[6]倪永年.化学计量学在分析化学中的应用.北京:科学出版社, 2004
[7]许禄,邵学广.化学计量学方法.第2版.北京:科学出版社, 2006
[8] Yu R Q. Chemometrics in China. Chemometrics and Intelligent Laboratory Systems, 1992, 14(1): 23-29
[9] Wold S. Chemometrics: what do we mean with it, and what do we want from it? Chemometrics and Intelligent Laboratory Systems, 1995, 30(1):109-115
[10] Kowalski B R. Analytical chemistry as an information science. Trends in Analytical Chemistry, 1981, 1(3): 71-74
[11] Brown S D, Barker T Q, Larivee R A, et al. Chemometrics. Analytical Chemistry, 1988, 60(12): 252-274
[12] Brown S D. Chemometrics. Analytical Chemistry, 1990, 62 (12): 84-101
[13] Brown S D, Bear R S, Blank Jr T B. Chemometrics. Analytical Chemistry, 1992, 64(12): 22-49
[14] Brown S D, Blank T B, Sum S T, et al. Chemometrics. Analytical Chemistry, 1994, 66(12): 315-359
[15] Brown S D, Sum S T, Despagne F, et al. Chemometrics. Analytical Chemistry, 1996, 68(12): 21-62
[16] Lavine B K. Chemometrics. Analytical Chemistry, 1998, 70(12): 209-228
[17] Lavine B K. Chemometrics. Analytical Chemistry, 2000, 72(12): 91-97
[18] Lavine B K, Workman J Jr. Chemometrics. Analytical Chemistry, 2002, 74(12): 2763-2769
[19] Lavine B K, Workman J Jr. Chemometrics. Analytical Chemistry, 2004, 76(12): 3365-3372
[20] Lavine B K, Workman J Jr. Chemometrics. Analytical Chemistry, 2006,78(12): 4137-4145
[21] Martens H, N?s T. Multivariate calibration. Chichester: John Wiley & Sons, 1989: 1-9
[22] Lorber A. Error propagation and figures of merit for quantification by solving matrix equations. Analytical Chemistry, 1986, 58(6):1167-1172
[23] Booksh K S, Kowalski B R. Theory of analytical chemistry. Analytical Chemistry, 1994, 66(15): 782-791
[24] Dief A S. Advanced matrix theory for scientists and engineers. Tunbridge Wells and London: Abacus Press, 1982: 93-94
[25] Stewart G W. Introduction to matrix computations. New York: Academic Press, 1973: 340-341
[26] Wold S, Martens H, Wold H. The multivariate calibration method in chemistry solved by the PLS method. Ruhe A, K?gstr?m B (eds). In: Proceedings on the Conference on Matrix Pencils, Lecture Notes in Mathematics. Heidelberg: Springer-Verlag, 1983: 286-293
[27] Hoskuldsson A. PLS regression methods. Journal of Chemometrics, 1988, 2: 211-228
[28] Druilhet P, Mom A. PLS regression: a directional signal-to-noise ratio approach. Journal of Multivariate Analysis, 2006, 97(6): 1313-1329
[29] Nadler B, Coifman R R. Partial least squares, Beer’s law and the net analyte signal: statistical modeling and analysis. Journal of Chemometrics, 2005, 19: 45-54
[30] Lorber A, Faber K, Kowalski B R. Net analyte signal calculation in multivariate calibration. Analytical Chemistry, 1997, 69(8): 1620-1626
[31] N?s A. The design of calibration in near infrared reflectance analysis by clustering. Journal of Chemometrics, 1987, 1: 121-134
[32] Zemroch P J. Cluster Analysis as an experimental design generator, with application to gasoline belending experiments. Technometrics, 1986, 28: 39-49
[33] Kennard R W, Stone L A. Computer aided design of experiments. Technometrics, 1969, 11: 137-148
[34] Honigs D, Hieftje G M, Mark H, Hirschfeld T B. Unique sample selection via near-infrared spectral subtraction. Analitical Chemistry, 1985, 57(12): 2299-2303
[35] Snee R D. Validation of regression models: methods and examples. Technometrics, 1977, 19(4): 415-428
[36] N?s T, Isaksson T, Fearn T, et al. A user-friendly guide to multivariate calibration and clsaaification. Chichester: NIR Publications, 2002: 192-193
[37] Spiegelman C H, McShane M J, Goetz M J, et al. Theoretical justification of wavelength selection in PLS calibration: development of a new algorithm. Analytical Chemistry, 1998, 70(1): 35-44
[38] Xie Y L, Liang Y Z, Yu R Q. Quantitative calibration of multi-component systems with a known range of possibly co-existing species. Analytica Chimica Acta, 1993, 272(1): 61-72
[39] N?rgaard L. A multivariate chemometric approach to fluorescence spectroscopy. Talanta, 1995, 42(9): 1305-1324
[40] Miller C E. The use of chemometric techniques in process analytical method development and operation. Chemometrics and Intelligent Laboratory Systems, 1995, 30(1): 11-22
[41] Spiegelman C, Wang S, Denham M. Asymptotic minimax calibration estimates. Chemometrics and Intelligent Laboratory Systems, 1996, 32(2): 257-263
[42] Jouan-Rimbaud D, Massart D L, de Noord O E. Random correlation in variable selection for multivariate calibration with a genetic algorithm. Chemometrics and Intelligent Laboratory Systems, 1996, 35(2): 213-220
[43] Xu L, Schechter L. Wavelength selection for simultaneous spectroscopic analysis. experimental and theoretical study. Analytical Chemistry, 1996, 68(17): 2392-2400
[44] Blasco F, Medina-Hernández M J, Sagrado S. Use of pH gradients in continuous-flow systems and multivariate regression techniques applied to the determination of methionine and cysteine in pharmaceuticals. Analytica Chimica Acta, 1997, 348(1-3): 151-159
[45] Walmsley A D. Improved variable selection procedure for multivariate linear regression. Analytica Chimica Acta, 1997, 354(1-3): 225-232
[46] Rupprecht M, Probst T. Development of a method for the systematic use of bilinear multivariate calibration methods for the correction of interferences in inductively coupled plasma-mass spectrometry. Analytica Chimica Acta, 1998, 358(3): 205-225
[47] Pasti L, Jouan-Rimbaud D, Massart D L, et al. Application of Fourier transform to multivariate calibration of near-infrared data. Analytica Chimica Acta, 1998, 364(1-3): 253-263
[48] Ding Q, Small G W. Genetic algorithm-based wavelength selection for thenear-infrared determination of glucose in biological matrixes: initialization strategies and effects of spectral resolution. Analytical Chemistry, 1998, 70(21): 4472-4479
[49] Forina M, Casolino M C, De la Pezuela Martinez C. Multivariate calibration: applications to pharmaceutical analysis. Journal of Pharmaceutical and Biomedical Analysis, 1998, 18(1-2): 21-33
[50] McShane M J, Cameron B D, CotéG L, et al. A novel peak-hopping stepwise feature selection method with application to Raman spectroscopy. Analytica Chimica Acta, 1999, 388(3): 251-264
[51] Norgaard L, Saudland A, Wagner J, et al.Interval partial least-squares regression (iPLS): a comparative chemometric study with an example from near-infrared spectroscopy. Applied Spectroscopy, 2000, 54(3): 413-419
[52] Zou X, Zhao J, Li Y. Selection of the efficient wavelength regions in FT-NIRspectroscopy for determination of SSC of‘Fuji’apple based on BiPLS and FiPLS models. Vibrational Spectroscopy, 2007, 44(2): 220-227
[53] Goicoechea H C, Olivieri A C. A new family of genetic algorithms for wavelength interval selection in multivariate analytical spectroscopy. Journal of Chemometrics, 2003, 17(6): 338-345
[54] Leardi R, N?rgaard L. Sequential application of backward interval partial least squares and genetic algorithms for the selection of relevant spectral regions. Journal of Chemometrics, 2004, 18(11): 486-497
[55] Jiang J H, Berry R J, Sielser H W, et al. Wavelength interval selection in multicomponent spectral analysis by moving window partial least-squares regression with applications to mid-infrared and near-infrared spectroscopic data. Analytical Chemistry, 2002, 74(14): 3555-3565
[56] Smith M R, Jee R D, Moffat A C, et al. Optimisation of partial least squares regression calibration models in near-infrared spectroscopy: a novel algorithm for wavelength selection. Analyst, 2003, 128: 1312-1319
[57] Du Y P, Liang Y Z, Jiang J H, et al. Spectral regions selection to improve prediction ability of PLS models by changeable size moving window partial least squares and searching combination moving window partial least squares. Analytica Chimica Acta, 2004, 501(2): 183-191
[58] Cramer J A, Kramer K E, Johnson K J, et al. Automated wavelength selection for spectroscopic fuel models by symmetrically contracting repeated unmoving window partial least squares. Chemometrics and Intelligent Laboratory Systems,2008, 92(1): 13-21
[59] Chau F T, Liang Y Z, Gao J, et al. Chemometrics: from basics to wavelet transform. Hoboken: John Wiley & Sons, 2004: 69-80
[60] Savitzky A, Golay M J E. Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry, 1964, 36(8): 1627-1639
[61] Geladi P, MacDougall D, Martens H. Linearization and scatter-correction for near-infrared reflectance spectra of meat. Applied Spectroscopy, 1985, 39(3): 491-500
[62] Barnes R J, Dhanoa M S, Lister, S J. Standard normal variate transformation and de-trending of near-infrared diffuse reflectance spectra. Applied Spectroscopy, 1989, 43(5): 772-777
[63] Wold S, Antti H, Lindgren F, et al. Orthogonal signal correction of near-infrared spectra. Chemometrics and Intelligent Laboratory Systems, 1998, 44(1-2): 175-185
[64] Mittermayr C R, Nikolov S G, Hutter H, et al. An introduction to wavelet transforms for chemometricians: a time-frequency approach. Chemometrics and Intelligent Laboratory Systems, 1997, 37(2): 215-239
[65] De Noord O E. Multivariate calibration standardization. Chemometrics and Intelligent Laboratory Systems, 1994, 25(2): 85-97
[66] Bouveresse E, Massart D L. Standardisation of near-infrared spectrometric instruments: a review. Vibrational Spectroscopy, 1996, 11(1): 3-15
[67] Fearn T. Standardisation and calibration transfer for near infrared instruments: a review. Journal of Near Infrared Spectroscopy, 2001, 9(4): 229-244
[68] Feudale R N, Woody N A, Tan H, et al. Transfer of multivariate calibration models: a review. Chemometrics and Intelligent Laboratory Systems, 2002, 64(2): 181-192
[69] Pereira C F, Pimentel M F, Galv?o R K H. A comparative study of calibration transfer methods for determination of gasoline quality parameters in three different near infrared spectrometers. Analytica Chimica Acta, 2008, 17(1): 41-47
[70] Kramer K E, Morris R E, Rose-Pehrsson S L. Comparison of two multiplicative signal correction strategies for calibration transfer without standards. Chemometrics and Intelligent Laboratory Systems, 2008, 92(1): 33-43
[71] Adhihetty I S, McGuire J A, Wangmaneerat B, et al. Achieving transferable multivariate spectral calibration models: demonstration with infrared spectra ofthin-film dielectrics on silicon. Analytical Chemistry, 1991, 63(20): 2329-2338
[72] De Noord O E. The influence of data preprocessing on the robustness and parsimony of multivariate calibration models. Chemometrics and Intelligent Laboratory Systems, 1994, 23(1): 65-70
[73] Ozdemir D, Mosley M, Williams R. Effect of wavelength drift on single- and multi-instrument calibration using genetic regression. Applied Spectroscopy, 1998, 52(9): 1203-1209
[74] Wülfert F, Kok W H, Smilde A K. Influence of Temperature on Vibrational Spectra and Consequences for the Predictive Ability of Multivariate Models. Analytical Chemistry, 1998, 70(9): 1761-1767
[75] Despagne F, Massart D L, Chabot P. Development of a robust calibration model for nonlinear in-line process data. Analytical Chemistry, 2000, 72(7): 1657-1665
[76] Stork C L, Kowalski B R. Weighting schemes for updating regression models—a theoretical approach. Chemometrics and Intelligent Laboratory Systems, 1999, 48(2): 151-166
[77] Swierenga H, De Weijer A P, Buydens L M C. Robust calibration model for on-line and off-line prediction of poly(ethylene terephthalate) yarn shrinkage by Raman spectroscopy. Journal of Chemometrics, 1999, 13(3-4): 237-249
[78] Greensill C V, Wolfs P J, Spiegelman C H, et al. Calibration transfer between PDA-based NIR spectrometers in the NIR assessment of melon soluble solids content. Applied Spectroscopy, 2001, 55(5): 647-653
[79] Mark H, workman Jr J. A new approach to generating transferable calibrations for quantitative near-infrared spectroscopy. Spectroscopy, 1988, 3(11): 28-36
[80] Swierenga H, De Groot P J, De Weijer A P, et al. Improvement of PLS model transferability by robust wavelength selection. Chemometrics and Intelligent Laboratory Systems, 1998, 41(2): 237-248
[81] Wang Y D, Veltkamp D J, Kowalski B K. Multivariate instrument standardization. Analytical Chemistry, 1991, 63(23): 2750-2756
[82] Forina M, Drava G, Armanino C, et al. Transfer of calibration function in near-infrared spectroscopy. Chemometrics and Intelligent Laboratory Systems, 1995, 27(2): 189-203
[83] Bouveresse E, Massart D L, Dardenne P. Modified algorithm for standardization of near-infrared spectrometric instruments. Analytical Chemistry, 1995, 67(8): 1381-1389
[84] Wang Z, Dean T, Kowalski B R. Additive background correction in multivariateinstrument standardization. Analytical Chemistry, 1995, 67(14): 2379-2385
[85] Jones J A, Last I R, MacDonald B F. Development and transferability of near-infrared methods for determination of moisture in a freeze-dried injection product. Journal of Pharmaceutical and Biomedical Analysis, 1993, 11(11-12): 1227-1231
[86] Bouveresse E, Hartmann C, Massart D L, et al. Standardization of Near-Infrared Spectrometric Instruments. Analytical Chemistry, 1996, 68(6): 982-990
[87] Kennedy J, Eberhart R. Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks. Perth, Australia, 1995: 1942-1948
[88] Eberhart R, Kennedy J. A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science. Nagoya, Japan, 1995, 39-43
[89] Kennedy J, Eberhart R A. Discrete binary version of the particle swarm algorithm. In: IEEE Int’1 Conference on Computational Cybernetics and Simulation, 1997, 4104-4108
[90] Shi Y, Eberhart R. A modified particle swarm optimizer. In: IEEE World Congress on Computational Intelligence, 1998, 69-73
[91] Carlisle A, Dozier G. Adapting particle swarm optimization to dynamic environments. In: Proceedings of Int’1 Conference on Artificial Intelligence. 2000, 429-434
[92] Shi Y, Eberhart R. Fuzzy adaptive particle swarm optimization. In: Proceedings of Congress on Evolutionary Computation. 2001, 79-85
[93] Clerc M, Kennedy J. The particle swarm-explosion, stability and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 2002, 6(1): 58-73
[94] Brandstatter B, Baumgartner U. Particle swarm optimization-mass-spring system analogon. IEEE Transactions on Magnetics, 2002, 38(2): 997-1000
[95] Angeline P J. Evolutionary optimization versus particle swarm optimization: Philosophy and performance differences. In: Evolutionary Programming VII, 1998, 601-610
[96] Clerc M. The swarm and the queen: Towards a deterministic and adaptive particle swarm optimization. In: Proceedings of the Congress of Evolutionary Computation. 1999, 1951-1957
[97] Ciuprina G, Loan D, Munteanu I. Use of intelligent-particle swarm optimizationin electromagnetics. IEEE Transactions on Magnetics, 2002, 38(2): 1037-1040
[98]李爱国,覃征,鲍复民.粒子群优化算法.计算机工程与应用, 2002, 38(21): 1-3
[99] Agrafiotis D K, Cedeno W. Feature selection for structure-activity correlation using binary particle swarms. Journal of Medicinal Chemistry, 2002, 45(5): 1098-1107
[100] Shen Q, Jiang J H, Yu R Q, et al. Modified particle swarm optimization algorithm for variable selection in MLR and PLS modeling: QSAR studies of antagonism of angiotensin II antagonists. European Journal of Pharmaceutical Sciences, 2004, 22(2-3): 145-152
[101] Wang Z, Durst G L, Eberhart R C, et al. Particle swarm optimization and neural network application for QSAR. In: Proceedings of IEEE International Conference on Parallel and Distributed Processing Symposium. 2004, 194-201
[102] Lin W Q, Jiang J H, Wu H L, et al. Recent advances in chemometric methodologies for QSAR studies. Current Computer-Aided Drug Design, 2006, 2(3): 255-266
[103] Breiman L. Bagging predictors. Machine Learning, 1996, 24(2): 123-140
[104] Schapire R E. The strength of weak learnability. Machine Learning, 1990, 5(2): 197-227
[105] Freund Y, Schapire R E. A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences, 1997, 55(1): 119-139
[106] Wolpert D. Stacked Generalization. Neural Networks, 1992, 5(2): 241-259
[107] Breiman L. Stacked Regressions. Machine Learning, 1996, 24(1): 49-64
[108] Mevik B H, Segtnan V H, N?s T. Ensemble methods and partial least squares regression. Journal of Chemometrics, 2004, 18(11): 498-507
[109] Zhang M H, Xu Q S, Massart D L. Averaged and weighted average partial least squares. Analytica Chimica Acta, 2004, 504(2): 279–289
[110] Zhang M H, Xu Q S, Massart D L. Boosting partial least squares. Analytical Chemistry, 2005, 77(5): 1423-1431
[111] Zhou Y P, Jiang J H, Wu H L, et al. Dry film method with ytterbium as the internal standard for near infrared spectroscopic plasma glucose assay coupled with boosting support vector regression. Journal of Chemometrics, 2006, 20(1-2): 13-21
[112] Shinzawa H, Jiang J H, Ritthiruangdej P, et al. Investigations of bagged kernelpartial least squares (KPLS) and boosting KPLS with applications to near-infrared (NIR) spectra. Journal of Chemometrics, 2006, 20(8-10): 436-444
[113] Galv?o P K H, Araújo M C U, Martins M D N, et al. An application of subagging for the improvement of prediction accuracy of multivariate calibration models. Chemometrics and Intelligent Laboratory Systems, 2006, 81(1): 60-67
[114] Chen D, Cai W S, Shao X G. Removing uncertain variables based on ensemble partial least squares. Analytica Chimica Acta, 2007, 598( 1): 19-26
[115] Han Q J, Wu H L, Cai C B, et al. An ensemble of Monte Carlo uninformative variable elimination for wavelength selection. Analytica Chimica Acta, 2008, 612( 2) : 121-125
[116] Vanbel P F, Tilquin B L, Schoenmakers P J. Criteria for developing rugged high-performance liquid chromatographic methods. Journal of Chromatography A, 1995, 697(1-2): 3-16
[117] Vanbel P F, Tilquin B L, Schoenmakers P J. Criteria for optimizing the separation of target analytes in complex chromatograms. Chemometrics and Intelligent Laboratory Systems, 1996, 35(1): 67-86
[118] Morris V M, Hughes J G, Marriott P J. Examination of a new chromatographic function, based on an exponential resolution term, for use in optimization strategies:application to capillary gas chromatography separation of phenols. Journal of Chromatography A, 1996, 755(2): 235-243
[119] Vanbel P F. Development of flexible and efficient strategies for optimizing chromatographic separations. Journal of Pharmaceutical and Biomedical Analysis, 1999, 21(3): 603-610
[120] Siouffi A M, Phan-Tan-Luu R. Optimization methods in chromatography and capillary electrophoresis. Journal of Chromatography A, 2000, 892(1-2): 75-106
[121] Sivakumar T, Manavalan R, Muralidharan C, et al. Multi-criteria decision making approach and experimental design as chemometric tools to optimize HPLC separationof domperidone and pantoprazole. Journal of Pharmaceutical and Biomedical Analysis, 2007, 43(5): 1842-1848
[122] Schoenmakers P J. Optimization of chromatographic selectivity. Amsterdam: Elsevier, 1986:1-5
[123] Xu Q S, Liang Y Z. Monte Carlo cross validation. Chemometrics and Intelligent Laboratory Systems, 2001, 56(1):1-11
[124] Gourvénec S, Pierna J A F, Massart D L. An evaluation of the PoLiSh smoothedregression and the Monte Carlo cross-validation for the determination of the complexity of a PLS model. Chemometrics and Intelligent Laboratory Systems, 2003, 68(1-2):41-51
[125] Gy P. Sampling for analytical purposes. New York: John Wiley & Sons, 1998: 1-10
[126] Petersen L, Minkkinen P, Esbensen K H. Representative sampling for reliable data analysis: theory of sampling. Chemometrics and Intelligent Laboratory Systems, 2005, 77(1-2): 261-277
[127] Worsfold P J, Gimbert L J, Mankasingh U, et al. Sampling, sample treatment and quality assurance issues for the determination of phosphorus species in natural waters and soils. Talanta, 2005, 66(2): 273-293
[128] Mark H. Comparative study of calibration methods for near-infrared reflectance analysis using a nested experimental design. Analytical Chemistry, 1986, 58(13): 2814-2819
[129] Devos O, Fanget B, Saber A I, et al. Use of a Plackett-Burman design with multivariate calibration for the analysis of polycyclic aromatic hydrocarbons in micellar media by synchronous fluorescence. Analytical Chemistry, 2002, 74(3): 678-683
[130] Borggaard C, Thodberg H H. Optimal minimal neural interpretation of spectra. Analytical Chemistry, 1992, 64(5): 545-551
[131] Wentzell P D, Andrews D T, Walsh J M, et al. Estimation of hydrocarbon types in light gas oils and diesel fuels by ultraviolet absorption spectroscopy and multivariate calibration. Canadian Journal of Chemistry, 1999, 77(3): 391-400
[132] Pedersen D K, Martens H, Nielsen J P, et al. Near-infrared absorption and scattering separated by extended inverted signal correction (EISC): analysis of near-infrared transmittance spectra of single wheat seeds. Applied Spectroscopy, 2002, 56(9): 1206-1214
[133] Lin J, Lo S C, Brown C W. Calibration transfer from a scanning near-IR spectrophotometer to a FT-near-IR spectrophotometer. Analytica Chimica Acta, 1997, 349(1-3): 263-269
[134] Swierenga W, Haanstra W G, De Weijer A P, et al. Comparison of two different approaches toward model transferability in NIR spectroscopy. Applied Spectroscopy, 1998, 52(1): 7-16
[135] Lin J. Near-IR calibration transfer between different temperatures. Applied Spectroscopy, 1998, 52(12): 1591-1596
[136] Wülfert F, Kok W T, de Noord O E, et al. Correction of temperature-induced spectral variation by continuous piecewise direct standardization. Analytical Chemistry, 2000, 72(7): 1639-1644
[137] Koehler F W, Small G W, Combs R J, et al. Calibration transfer algorithm for automated qualitative analysis by passive fourier transform infrared spectrometry. Analytical Chemistry, 2000, 72(7): 1690-1698
[138] Walczak B, Bouveresse E, Massar D L. Standardization of near-infrared spectra in the wavelet domain. Chemometrics and Intelligent Laboratory Systems, 1997, 36(1): 41-51
[139] Blanco M, Coello J, Iturriaga H, et al. Effect of data preprocessing methods in near-infrared diffuse reflectance spectroscopy for the determination of the active compound in a pharmaceutical preparation. Applied Spectroscopy, 1997, 51(2): 240-246
[140] Derringer G,Suich R. Simultaneous optimization of several response variables. Journal of Quality Technology, 1980, 12(4): 214-219
[141] Liang Y Z, Xie P S, Chan K. Quality control of herbal medicines. Journal of Chromatography B, 2004, 812(1-2): 53-70
[142] de Juan A, Tauler R. Chemometrics applied to unravel multicomponent processes and mixtures Revisiting latest trends in multivariate resolution. Analytica Chimica Acta, 2003, 500(1-2): 195-210
[143] Jiang J H, Liang Y Z, Ozaki Y. Principles and methodologies in self-modeling curve resolution. Chemometrics and Intelligent Laboratory Systems, 2004, 71(1): 1-12
[144] de Juan A, Tauler R. Factor analysis of hyphenated chromatographic data exploration, resolution and quantification of multicomponent systems. Journal of Chromatography A, 2007, 1158(1-2): 184-195
[145] Kvalheim O M, Liang Y Z. Heuristic evolving latent projections: resolving two-way multicomponent data. 1. Selectivity, latent-projective graph, datascope, local rank, and unique resolution. Analytical Chemistry, 1992, 64(8): 936-946
[146] Liang Y Z, Kvalheim O M, Keller H R, et al. Heuristic evolving latent projections: resolving two-way multicomponent data. 2. Detection and resolution of minor constituents. Analytical Chemistry, 1992, 64(8): 946-953
[147] Tauler R, Smilde A, Kowalski B. Selectivity, local rank, three-way data analysis and ambiguity in multivariate curve resolution. Journal of Chemometrics, 1995, 9(1): 31-58
[148] Levina E, Wagaman A S, Callender A F, et al. Estimating the number of purechemical components in a mixture by maximum likelihood. Journal of Chemometrics, 2007, 21(1-2): 24-34
[149] Shen H L, Wang J H, Liang Y Z, et al. Chemical rank estimation by multiresolution analysis for two-way data in the presence of background. Chemometrics and Intelligent Laboratory Systems, 1997, 37( 2): 261-269
[150] Shao X G, Cai W S, Sun P Y. Determination of the component number in overlapping multicomponent chromatogram using wavelet transform. Chemometrics and Intelligent Laboratory Systems, 1998, 43(1-2): 147-155
[151] Malinowski E R. Factor Analysis in Chemistry (third ed.). New York: Wiley, 2002: 73-111
[152] Elbergali A, Nygren J, Kubista M. An automated procedure to predict the number of components in spectroscopic data. Analytica Chimica Acta, 1999, 379(1-2): 143-158
[153] Meloun M, ?apek J, Mik?ík P, et al. Critical comparison of methods predicting the number of components in spectroscopic data. Analytica Chimica Acta, 2000, 423(1): 51-68
[154] Fruchter B. Introduction to Factor Analysis. New York: Van Nostrand, 1954: 1-10
[155] Comrey A L. A First Course in Factor Analysis. Orlando: Academic, 1973: 1-5
[156] Hugus Jr. Z Z, El-Awady A A. The determination of the number of species present in a system: A new matrix rank treatment of spectrophotometric data. Journal of Physical Chemistry, 1971, 75(19): 2954-2957
[157] Ritter G l, Lowry S R, Isenhour T L, et al. Factor analysis of the mass spectra of mixtures. Analytical Chemistry, 1976,48(3): 591-595
[158] Kankare J J. Computation of equilibrium constants for multicomponent systems from spectrophotometric data. Analytical Chemistry, 1970, 42(12): 1322-1326
[159] Wallace R M, Katz S M. A method for the determination of rank in the analysis of absorption spectra of multicomponent systems. Journal of Physical Chemistry, 1964, 68(12): 3890-3892
[160] Kaiser H F. The application of electronic computers to factor analysis. Educational and Psychological Measurement, 1960, 20(1): 141-151
[161] Kindsvanter J H, Weiner P H, Klingen T J. Correlation of retention volumes of substitutued carboranes with molecular properties in high pressure liquid chromatography using factor analysis. Analytical Chemistry, 1974, 46(8): 982-988
[162] Chen Z P, Liang Y Z, Jiang J H, et al. Determination of the number of components in mixtures using a new approach incorporating chemical information. Journal of Chemometrics, 1999, 13(1): 15-30
[163] Silverman B W. Smoothed functional principal components analysis by choice of norm. Annals of Statistics, 1996, 24(1): 1-24
[164] Wang J H, Liang Y Z, Jiang J H, et al. Local chemical rank estimation of two-way data in the presence of heteroscedastic noise: A morphological approach. Chemometrics and Intelligent Laboratory Systems, 1996, 32(2): 265-272
[165] Shen H L, Stordrange L, Manne R, et al. The morphological score and its application to chemical rank determination. Chemometrics and Intelligent Laboratory Systems, 2000, 51(1): 37-47
[166] Cattell R B. Extracting the correct number of factors in factor analysis. Educational and Psychological Measurement, 1958, 18(4): 791-838
[167] Shrager R I, Hendler R W. Titration of individual components in a mixture with resolution of difference spectra, pKs, and redox transitions. Analytical Chemistry, 1982, 54(7): 1147-1152
[168] Rossi T M, Warner I M. Rank estimation of emission excitation matrixes using frequency analysis of eigenvectors. Analytical Chemistry, 1986, 58(4): 810-815
[169] Tu X M, Burdick D S, Millican D W, et al. Canonical correlation technique for rank estimation of excitation-emission matrixes. Analytical Chemistry, 1989, 61(19): 2219-2224
[170] Shen H L, Liang Y Z, Kvalheim O M, et al. Determination of chemical rank of two-way data from mixtures using subspace comparisons. Chemometrics and Intelligent Laboratory Systems, 2000, 51(1): 49-59
[171] Malinowski E R. Determination of the number of factors and the experimental error in a data matrix. Analytical Chemistry, 1977, 49(4): 612-617
[172] Wold S. Cross-validatory estimation of the number of components in factor and principal components models. Technometrics, 1978, 20(4): 397-405
[173] Malinowski E R. Statistical F-tests for abstract factor analysis and target testing. Journal of Chemometrics, 2005, 3(1): 49-60
[174] Faber K, Kowalski B R. Modification of Malinowski's F-test for abstract factor analysis applied to the Quail Roost II data sets. Journal of Chemometrics, 1997, 11( 1): 53-72
[175] Malinowski E R. Abstract factor analysis of data with multiple sources of errorand a modified Faber-Kowalski f-test. Journal of Chemometrics, 1999, 13(2): 69-81
[176] Ohta N. Estimating absorption bands of component dyes by means of principal component analysis. Analytical Chemistry, 1973, 45(3): 553-557
[177] Sharaf M A, Kowalski B R. Quantitative resolution of fused chromatographic peaks in gas chromatography/mass spectrometry. Analytical Chemistry, 1982, 54(8): 1291-1296
[178] Gampp H, Maeder M, Meyer C J, et al. Calculation of equilibrium constants from multiwavelength spectroscopic data—III model-free analysis of spectrophotometric and ESR titrations. Talanta, 1985, 32 (12): 1133-1139
[179] Maeder M. Evolving factor analysis for the resolution of overlapping chromatographic peaks. Analytical Chemistry, 1987, 59(3): 527-530
[180] Keller H R, Massart D L. Peak purity control in liquid chromatography with photodiode-array detection by a fixed size moving window evolving factor analysis. Analytica Chimica Acta, 1991, 246(2): 379-390
[181] Ritter C, Gilliard J A, Cumps J, et al. Corrections for heteroscedasticity in window evolving factor analysis. Analytica Chimica Acta, 1996, 318(2): 125-136
[182] Alsberg B K. Properties of local rank map vectors from multidetection chromatograms. Analytica Chimica Acta, 1996, 318(2): 137-150
[183] Whitson A C, Maeder M. Exhaustive evolving factor analysis (E-EFA). Journal of Chemometrics, 2001, 15(5): 475-484
[184] Zeng Z D, Xu C J, Liang Y Z, et al. Sectional moving window factor analysis for diagnosing elution chromatographic patterns. Chemometrics and Intelligent Laboratory Systems, 2003, 69(1-2): 89-101
[185] Chen Z P, Morris J, Martin E, et al. Recursive evolving spectral projection for revealing the concentration windows of overlapping peaks in two-way chromatographic experiments. Chemometrics and Intelligent Laboratory Systems, 2004, 72(1): 9-19
[186] Toft J, Kvalheim O M. Eigenstructure tracking analysis for revealing noise pattern and local rank in instrumental profiles: Application to transmittance and absorbance IR spectroscopy. Chemometrics and Intelligent Laboratory Systems, 1993, 19(1): 65-73
[187] Sánchez F C, Van Den Bogaert B, Rutan S C, et al. Multivariate peak purity approaches. Chemometrics and Intelligent Laboratory Systems, 1996, 34(2):139-171
[188] Rodríguez-Cuesta M J, BoquéR, Rius F X, et al. Development and validation of a method for determining pesticides in groundwater from complex overlapped HPLC signals and multivariate curve resolution. Chemometrics and Intelligent Laboratory Systems,2005, 77(1-2): 251-260
[189] Windig W, Guilment J. Interactive self-modeling mixture analysis. Analytical Chemistry, 1991, 63(14): 1425-1432
[190] Windig W, Heckler C E. Self-modeling mixture analysis of categorized pyrolysis mass spectral data with the SIMPLISMA approach. Chemometrics and Intelligent Laboratory Systems, 1992, 14(1-3): 195-207
[191] Sánchez F C, Massart D L. Application of SIMPLISMA for the assessment of peak purity in liquid chromatography with diode array detection. Analytica Chimica Acta, 1994, 298(3): 331-339
[192] Sánchez FC, Toft J, Van Den Bogaert B, et al. Orthogonal projection approach applied to peak purity assessment. Analytical Chemistry, 1996, 68 (1): 79-85
[193] Gemperline P J. A priori estimates of the elution profiles of the pure components in overlapped liquid chromatography peaks using target factor analysis. Journal of Chemical Information and Computer Sciences, 1984, 24(4): 206 - 212
[194] Fabre H, Le Bris A, Blanchin M D. Evaluation of different techniques for peak purity assessment on a diode-array detector in liquid chromatography. Journal of Chromatography A, 1995, 697(1-2): 81-88
[195] Bylund D, Danielsson R, Markides K E. Peak purity assessment in liquid chromatography-mass spectrometry. Journal of Chromatography A, 2001, 915(1-2): 43-52
[196] Arvis T D, Kalivas J H. Fundamentals of condition index evolving profiles for qualitative analysis of unresolved chromatographic peaks. Analytica Chimica Acta, 1992, 266(1): 13-24
[197] Bakken G A, Kalivas J H. Assessing chromatographic peak purity using condition index and singular value evolving profiles. Analytica Chimica Acta, 1995, 300(1-3): 173-181
[198] Vanslyke S J, Wentzell P D. Real-time principal component analysis using parallel Kalman filter networks for peak purity analysis. Analytical Chemistry, 1991, 63(21): 2512-2519
[199] Hopke P K, Alpert D J, Roscoe B A. Fantasia-a program for target transformation factor analysis to apportion sources in environmental samples.Computers and Chemistry, 1983, 7(3): 149-155
[200] Vandeginste B G M, Derks W, Kateman G. Multicomponent self-modelling curve resolution in high-performance liquid chromatography by iterative target transformation analysis. Analytica Chimica Acta, 1985, 173: 253-264
[201] De Juan A, Van Den Bogaert B, Sánchez F C, et al. Application of the needle algorithm for exploratory analysis and resolution of HPLC-DAD data. Chemometrics and Intelligent Laboratory Systems, 1996, 33(2): 133-145
[202] Xie Y L, Baeza-Baeza J J, Ramis-Ramos G. Assessment of peak purity in liquid chromatography using condition index and singular value evolving profiles. Analytica Chimica Acta, 1995, 317(1-3): 17-32
[203] Wiberg K, Andersson M, Hagman A, et al. Peak purity determination with principal component analysis of high-performance liquid chromatography-diode array detection data. Journal of Chromatography A, 2004, 1029(1-2): 13-20
[204] Polster J, Sauerwald N, Feucht W, et al. New methods for spectrometric peak purity analysis in chromatography. Journal of Chromatography A, 1998, 800(2): 121-133
[205] Gilliard J A, Ritter C. Use of simulated liquid chromatography-diode array detection data for the definition of a guide curve in peak purity assessment by spectral comparison. Journal of Chromatography A, 1997,786(1): 1-11
[206] Gong F, Liang Y Z, Xu Q S, et al. Evaluation of separation quality in two-dimensional hyphenated chromatography. Analytica Chimica Acta, 2001, 450(1-2): 99-114
[207] Malinowski E R. Obtaining the key set of typical vectors by factor analysis and subsequent isolation of component spectra. Analytica Chimica Acta, 1982, 134: 129-137
[208] Faber K, Lorber A, Kowalski B R. Analytical figures of merit for tensorial calibration. Journal of Chemometrics, 1997, 11(5): 419-461
[209] Messick N J, Kalivas J H, Lang P M. Selectivity and related measures for nth-order data. Analytical Chemistry, 1996, 68(9): 1572-1579
[210] Vivó-Truyols G, Torres-LapasióJ R, García-Alvarez-Coque M C. Net analyte signal as a deconvolution-oriented resolution criterion in the optimisation of chromatographic techniques. Journal of Chromatography A, 2003, 991(1): 47-59
[211] Faber N M. Exact presentation of multivariate calibration model as univariate calibration graph. Chemometrics and Intelligent Laboratory Systems, 2000,50(1): 107-114
[212] Duewer D L, Kowalski B R, Fasching J L. Improving the reliability of factor analysis of chemical data by utilizing the measured analytical uncertainty. Analytical Chemistry, 1976, 48(13): 2002-2010
[213] Daszykowski M, Walczak B. Use and abuse of chemometrics in chromatography. Trends in Analytical Chemistry, 2006, 25(11): 1081-1096
[2]高鸿.分析化学前沿.北京:科学出版社, 1991
[3]梁逸曾.白灰黑复杂多组分分析体系及其化学计量学算法.长沙:湖南科技出版社, 1997
[4]陆晓华.化学计量学.武汉:华中理工大学出版社, 1997
[5]梁逸曾,俞汝勤.分析化学手册(第十分册)化学计量学.北京:化工出版社, 2000
[6]倪永年.化学计量学在分析化学中的应用.北京:科学出版社, 2004
[7]许禄,邵学广.化学计量学方法.第2版.北京:科学出版社, 2006
[8] Yu R Q. Chemometrics in China. Chemometrics and Intelligent Laboratory Systems, 1992, 14(1): 23-29
[9] Wold S. Chemometrics: what do we mean with it, and what do we want from it? Chemometrics and Intelligent Laboratory Systems, 1995, 30(1):109-115
[10] Kowalski B R. Analytical chemistry as an information science. Trends in Analytical Chemistry, 1981, 1(3): 71-74
[11] Brown S D, Barker T Q, Larivee R A, et al. Chemometrics. Analytical Chemistry, 1988, 60(12): 252-274
[12] Brown S D. Chemometrics. Analytical Chemistry, 1990, 62 (12): 84-101
[13] Brown S D, Bear R S, Blank Jr T B. Chemometrics. Analytical Chemistry, 1992, 64(12): 22-49
[14] Brown S D, Blank T B, Sum S T, et al. Chemometrics. Analytical Chemistry, 1994, 66(12): 315-359
[15] Brown S D, Sum S T, Despagne F, et al. Chemometrics. Analytical Chemistry, 1996, 68(12): 21-62
[16] Lavine B K. Chemometrics. Analytical Chemistry, 1998, 70(12): 209-228
[17] Lavine B K. Chemometrics. Analytical Chemistry, 2000, 72(12): 91-97
[18] Lavine B K, Workman J Jr. Chemometrics. Analytical Chemistry, 2002, 74(12): 2763-2769
[19] Lavine B K, Workman J Jr. Chemometrics. Analytical Chemistry, 2004, 76(12): 3365-3372
[20] Lavine B K, Workman J Jr. Chemometrics. Analytical Chemistry, 2006,78(12): 4137-4145
[21] Martens H, N?s T. Multivariate calibration. Chichester: John Wiley & Sons, 1989: 1-9
[22] Lorber A. Error propagation and figures of merit for quantification by solving matrix equations. Analytical Chemistry, 1986, 58(6):1167-1172
[23] Booksh K S, Kowalski B R. Theory of analytical chemistry. Analytical Chemistry, 1994, 66(15): 782-791
[24] Dief A S. Advanced matrix theory for scientists and engineers. Tunbridge Wells and London: Abacus Press, 1982: 93-94
[25] Stewart G W. Introduction to matrix computations. New York: Academic Press, 1973: 340-341
[26] Wold S, Martens H, Wold H. The multivariate calibration method in chemistry solved by the PLS method. Ruhe A, K?gstr?m B (eds). In: Proceedings on the Conference on Matrix Pencils, Lecture Notes in Mathematics. Heidelberg: Springer-Verlag, 1983: 286-293
[27] Hoskuldsson A. PLS regression methods. Journal of Chemometrics, 1988, 2: 211-228
[28] Druilhet P, Mom A. PLS regression: a directional signal-to-noise ratio approach. Journal of Multivariate Analysis, 2006, 97(6): 1313-1329
[29] Nadler B, Coifman R R. Partial least squares, Beer’s law and the net analyte signal: statistical modeling and analysis. Journal of Chemometrics, 2005, 19: 45-54
[30] Lorber A, Faber K, Kowalski B R. Net analyte signal calculation in multivariate calibration. Analytical Chemistry, 1997, 69(8): 1620-1626
[31] N?s A. The design of calibration in near infrared reflectance analysis by clustering. Journal of Chemometrics, 1987, 1: 121-134
[32] Zemroch P J. Cluster Analysis as an experimental design generator, with application to gasoline belending experiments. Technometrics, 1986, 28: 39-49
[33] Kennard R W, Stone L A. Computer aided design of experiments. Technometrics, 1969, 11: 137-148
[34] Honigs D, Hieftje G M, Mark H, Hirschfeld T B. Unique sample selection via near-infrared spectral subtraction. Analitical Chemistry, 1985, 57(12): 2299-2303
[35] Snee R D. Validation of regression models: methods and examples. Technometrics, 1977, 19(4): 415-428
[36] N?s T, Isaksson T, Fearn T, et al. A user-friendly guide to multivariate calibration and clsaaification. Chichester: NIR Publications, 2002: 192-193
[37] Spiegelman C H, McShane M J, Goetz M J, et al. Theoretical justification of wavelength selection in PLS calibration: development of a new algorithm. Analytical Chemistry, 1998, 70(1): 35-44
[38] Xie Y L, Liang Y Z, Yu R Q. Quantitative calibration of multi-component systems with a known range of possibly co-existing species. Analytica Chimica Acta, 1993, 272(1): 61-72
[39] N?rgaard L. A multivariate chemometric approach to fluorescence spectroscopy. Talanta, 1995, 42(9): 1305-1324
[40] Miller C E. The use of chemometric techniques in process analytical method development and operation. Chemometrics and Intelligent Laboratory Systems, 1995, 30(1): 11-22
[41] Spiegelman C, Wang S, Denham M. Asymptotic minimax calibration estimates. Chemometrics and Intelligent Laboratory Systems, 1996, 32(2): 257-263
[42] Jouan-Rimbaud D, Massart D L, de Noord O E. Random correlation in variable selection for multivariate calibration with a genetic algorithm. Chemometrics and Intelligent Laboratory Systems, 1996, 35(2): 213-220
[43] Xu L, Schechter L. Wavelength selection for simultaneous spectroscopic analysis. experimental and theoretical study. Analytical Chemistry, 1996, 68(17): 2392-2400
[44] Blasco F, Medina-Hernández M J, Sagrado S. Use of pH gradients in continuous-flow systems and multivariate regression techniques applied to the determination of methionine and cysteine in pharmaceuticals. Analytica Chimica Acta, 1997, 348(1-3): 151-159
[45] Walmsley A D. Improved variable selection procedure for multivariate linear regression. Analytica Chimica Acta, 1997, 354(1-3): 225-232
[46] Rupprecht M, Probst T. Development of a method for the systematic use of bilinear multivariate calibration methods for the correction of interferences in inductively coupled plasma-mass spectrometry. Analytica Chimica Acta, 1998, 358(3): 205-225
[47] Pasti L, Jouan-Rimbaud D, Massart D L, et al. Application of Fourier transform to multivariate calibration of near-infrared data. Analytica Chimica Acta, 1998, 364(1-3): 253-263
[48] Ding Q, Small G W. Genetic algorithm-based wavelength selection for thenear-infrared determination of glucose in biological matrixes: initialization strategies and effects of spectral resolution. Analytical Chemistry, 1998, 70(21): 4472-4479
[49] Forina M, Casolino M C, De la Pezuela Martinez C. Multivariate calibration: applications to pharmaceutical analysis. Journal of Pharmaceutical and Biomedical Analysis, 1998, 18(1-2): 21-33
[50] McShane M J, Cameron B D, CotéG L, et al. A novel peak-hopping stepwise feature selection method with application to Raman spectroscopy. Analytica Chimica Acta, 1999, 388(3): 251-264
[51] Norgaard L, Saudland A, Wagner J, et al.Interval partial least-squares regression (iPLS): a comparative chemometric study with an example from near-infrared spectroscopy. Applied Spectroscopy, 2000, 54(3): 413-419
[52] Zou X, Zhao J, Li Y. Selection of the efficient wavelength regions in FT-NIRspectroscopy for determination of SSC of‘Fuji’apple based on BiPLS and FiPLS models. Vibrational Spectroscopy, 2007, 44(2): 220-227
[53] Goicoechea H C, Olivieri A C. A new family of genetic algorithms for wavelength interval selection in multivariate analytical spectroscopy. Journal of Chemometrics, 2003, 17(6): 338-345
[54] Leardi R, N?rgaard L. Sequential application of backward interval partial least squares and genetic algorithms for the selection of relevant spectral regions. Journal of Chemometrics, 2004, 18(11): 486-497
[55] Jiang J H, Berry R J, Sielser H W, et al. Wavelength interval selection in multicomponent spectral analysis by moving window partial least-squares regression with applications to mid-infrared and near-infrared spectroscopic data. Analytical Chemistry, 2002, 74(14): 3555-3565
[56] Smith M R, Jee R D, Moffat A C, et al. Optimisation of partial least squares regression calibration models in near-infrared spectroscopy: a novel algorithm for wavelength selection. Analyst, 2003, 128: 1312-1319
[57] Du Y P, Liang Y Z, Jiang J H, et al. Spectral regions selection to improve prediction ability of PLS models by changeable size moving window partial least squares and searching combination moving window partial least squares. Analytica Chimica Acta, 2004, 501(2): 183-191
[58] Cramer J A, Kramer K E, Johnson K J, et al. Automated wavelength selection for spectroscopic fuel models by symmetrically contracting repeated unmoving window partial least squares. Chemometrics and Intelligent Laboratory Systems,2008, 92(1): 13-21
[59] Chau F T, Liang Y Z, Gao J, et al. Chemometrics: from basics to wavelet transform. Hoboken: John Wiley & Sons, 2004: 69-80
[60] Savitzky A, Golay M J E. Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry, 1964, 36(8): 1627-1639
[61] Geladi P, MacDougall D, Martens H. Linearization and scatter-correction for near-infrared reflectance spectra of meat. Applied Spectroscopy, 1985, 39(3): 491-500
[62] Barnes R J, Dhanoa M S, Lister, S J. Standard normal variate transformation and de-trending of near-infrared diffuse reflectance spectra. Applied Spectroscopy, 1989, 43(5): 772-777
[63] Wold S, Antti H, Lindgren F, et al. Orthogonal signal correction of near-infrared spectra. Chemometrics and Intelligent Laboratory Systems, 1998, 44(1-2): 175-185
[64] Mittermayr C R, Nikolov S G, Hutter H, et al. An introduction to wavelet transforms for chemometricians: a time-frequency approach. Chemometrics and Intelligent Laboratory Systems, 1997, 37(2): 215-239
[65] De Noord O E. Multivariate calibration standardization. Chemometrics and Intelligent Laboratory Systems, 1994, 25(2): 85-97
[66] Bouveresse E, Massart D L. Standardisation of near-infrared spectrometric instruments: a review. Vibrational Spectroscopy, 1996, 11(1): 3-15
[67] Fearn T. Standardisation and calibration transfer for near infrared instruments: a review. Journal of Near Infrared Spectroscopy, 2001, 9(4): 229-244
[68] Feudale R N, Woody N A, Tan H, et al. Transfer of multivariate calibration models: a review. Chemometrics and Intelligent Laboratory Systems, 2002, 64(2): 181-192
[69] Pereira C F, Pimentel M F, Galv?o R K H. A comparative study of calibration transfer methods for determination of gasoline quality parameters in three different near infrared spectrometers. Analytica Chimica Acta, 2008, 17(1): 41-47
[70] Kramer K E, Morris R E, Rose-Pehrsson S L. Comparison of two multiplicative signal correction strategies for calibration transfer without standards. Chemometrics and Intelligent Laboratory Systems, 2008, 92(1): 33-43
[71] Adhihetty I S, McGuire J A, Wangmaneerat B, et al. Achieving transferable multivariate spectral calibration models: demonstration with infrared spectra ofthin-film dielectrics on silicon. Analytical Chemistry, 1991, 63(20): 2329-2338
[72] De Noord O E. The influence of data preprocessing on the robustness and parsimony of multivariate calibration models. Chemometrics and Intelligent Laboratory Systems, 1994, 23(1): 65-70
[73] Ozdemir D, Mosley M, Williams R. Effect of wavelength drift on single- and multi-instrument calibration using genetic regression. Applied Spectroscopy, 1998, 52(9): 1203-1209
[74] Wülfert F, Kok W H, Smilde A K. Influence of Temperature on Vibrational Spectra and Consequences for the Predictive Ability of Multivariate Models. Analytical Chemistry, 1998, 70(9): 1761-1767
[75] Despagne F, Massart D L, Chabot P. Development of a robust calibration model for nonlinear in-line process data. Analytical Chemistry, 2000, 72(7): 1657-1665
[76] Stork C L, Kowalski B R. Weighting schemes for updating regression models—a theoretical approach. Chemometrics and Intelligent Laboratory Systems, 1999, 48(2): 151-166
[77] Swierenga H, De Weijer A P, Buydens L M C. Robust calibration model for on-line and off-line prediction of poly(ethylene terephthalate) yarn shrinkage by Raman spectroscopy. Journal of Chemometrics, 1999, 13(3-4): 237-249
[78] Greensill C V, Wolfs P J, Spiegelman C H, et al. Calibration transfer between PDA-based NIR spectrometers in the NIR assessment of melon soluble solids content. Applied Spectroscopy, 2001, 55(5): 647-653
[79] Mark H, workman Jr J. A new approach to generating transferable calibrations for quantitative near-infrared spectroscopy. Spectroscopy, 1988, 3(11): 28-36
[80] Swierenga H, De Groot P J, De Weijer A P, et al. Improvement of PLS model transferability by robust wavelength selection. Chemometrics and Intelligent Laboratory Systems, 1998, 41(2): 237-248
[81] Wang Y D, Veltkamp D J, Kowalski B K. Multivariate instrument standardization. Analytical Chemistry, 1991, 63(23): 2750-2756
[82] Forina M, Drava G, Armanino C, et al. Transfer of calibration function in near-infrared spectroscopy. Chemometrics and Intelligent Laboratory Systems, 1995, 27(2): 189-203
[83] Bouveresse E, Massart D L, Dardenne P. Modified algorithm for standardization of near-infrared spectrometric instruments. Analytical Chemistry, 1995, 67(8): 1381-1389
[84] Wang Z, Dean T, Kowalski B R. Additive background correction in multivariateinstrument standardization. Analytical Chemistry, 1995, 67(14): 2379-2385
[85] Jones J A, Last I R, MacDonald B F. Development and transferability of near-infrared methods for determination of moisture in a freeze-dried injection product. Journal of Pharmaceutical and Biomedical Analysis, 1993, 11(11-12): 1227-1231
[86] Bouveresse E, Hartmann C, Massart D L, et al. Standardization of Near-Infrared Spectrometric Instruments. Analytical Chemistry, 1996, 68(6): 982-990
[87] Kennedy J, Eberhart R. Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks. Perth, Australia, 1995: 1942-1948
[88] Eberhart R, Kennedy J. A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science. Nagoya, Japan, 1995, 39-43
[89] Kennedy J, Eberhart R A. Discrete binary version of the particle swarm algorithm. In: IEEE Int’1 Conference on Computational Cybernetics and Simulation, 1997, 4104-4108
[90] Shi Y, Eberhart R. A modified particle swarm optimizer. In: IEEE World Congress on Computational Intelligence, 1998, 69-73
[91] Carlisle A, Dozier G. Adapting particle swarm optimization to dynamic environments. In: Proceedings of Int’1 Conference on Artificial Intelligence. 2000, 429-434
[92] Shi Y, Eberhart R. Fuzzy adaptive particle swarm optimization. In: Proceedings of Congress on Evolutionary Computation. 2001, 79-85
[93] Clerc M, Kennedy J. The particle swarm-explosion, stability and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 2002, 6(1): 58-73
[94] Brandstatter B, Baumgartner U. Particle swarm optimization-mass-spring system analogon. IEEE Transactions on Magnetics, 2002, 38(2): 997-1000
[95] Angeline P J. Evolutionary optimization versus particle swarm optimization: Philosophy and performance differences. In: Evolutionary Programming VII, 1998, 601-610
[96] Clerc M. The swarm and the queen: Towards a deterministic and adaptive particle swarm optimization. In: Proceedings of the Congress of Evolutionary Computation. 1999, 1951-1957
[97] Ciuprina G, Loan D, Munteanu I. Use of intelligent-particle swarm optimizationin electromagnetics. IEEE Transactions on Magnetics, 2002, 38(2): 1037-1040
[98]李爱国,覃征,鲍复民.粒子群优化算法.计算机工程与应用, 2002, 38(21): 1-3
[99] Agrafiotis D K, Cedeno W. Feature selection for structure-activity correlation using binary particle swarms. Journal of Medicinal Chemistry, 2002, 45(5): 1098-1107
[100] Shen Q, Jiang J H, Yu R Q, et al. Modified particle swarm optimization algorithm for variable selection in MLR and PLS modeling: QSAR studies of antagonism of angiotensin II antagonists. European Journal of Pharmaceutical Sciences, 2004, 22(2-3): 145-152
[101] Wang Z, Durst G L, Eberhart R C, et al. Particle swarm optimization and neural network application for QSAR. In: Proceedings of IEEE International Conference on Parallel and Distributed Processing Symposium. 2004, 194-201
[102] Lin W Q, Jiang J H, Wu H L, et al. Recent advances in chemometric methodologies for QSAR studies. Current Computer-Aided Drug Design, 2006, 2(3): 255-266
[103] Breiman L. Bagging predictors. Machine Learning, 1996, 24(2): 123-140
[104] Schapire R E. The strength of weak learnability. Machine Learning, 1990, 5(2): 197-227
[105] Freund Y, Schapire R E. A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences, 1997, 55(1): 119-139
[106] Wolpert D. Stacked Generalization. Neural Networks, 1992, 5(2): 241-259
[107] Breiman L. Stacked Regressions. Machine Learning, 1996, 24(1): 49-64
[108] Mevik B H, Segtnan V H, N?s T. Ensemble methods and partial least squares regression. Journal of Chemometrics, 2004, 18(11): 498-507
[109] Zhang M H, Xu Q S, Massart D L. Averaged and weighted average partial least squares. Analytica Chimica Acta, 2004, 504(2): 279–289
[110] Zhang M H, Xu Q S, Massart D L. Boosting partial least squares. Analytical Chemistry, 2005, 77(5): 1423-1431
[111] Zhou Y P, Jiang J H, Wu H L, et al. Dry film method with ytterbium as the internal standard for near infrared spectroscopic plasma glucose assay coupled with boosting support vector regression. Journal of Chemometrics, 2006, 20(1-2): 13-21
[112] Shinzawa H, Jiang J H, Ritthiruangdej P, et al. Investigations of bagged kernelpartial least squares (KPLS) and boosting KPLS with applications to near-infrared (NIR) spectra. Journal of Chemometrics, 2006, 20(8-10): 436-444
[113] Galv?o P K H, Araújo M C U, Martins M D N, et al. An application of subagging for the improvement of prediction accuracy of multivariate calibration models. Chemometrics and Intelligent Laboratory Systems, 2006, 81(1): 60-67
[114] Chen D, Cai W S, Shao X G. Removing uncertain variables based on ensemble partial least squares. Analytica Chimica Acta, 2007, 598( 1): 19-26
[115] Han Q J, Wu H L, Cai C B, et al. An ensemble of Monte Carlo uninformative variable elimination for wavelength selection. Analytica Chimica Acta, 2008, 612( 2) : 121-125
[116] Vanbel P F, Tilquin B L, Schoenmakers P J. Criteria for developing rugged high-performance liquid chromatographic methods. Journal of Chromatography A, 1995, 697(1-2): 3-16
[117] Vanbel P F, Tilquin B L, Schoenmakers P J. Criteria for optimizing the separation of target analytes in complex chromatograms. Chemometrics and Intelligent Laboratory Systems, 1996, 35(1): 67-86
[118] Morris V M, Hughes J G, Marriott P J. Examination of a new chromatographic function, based on an exponential resolution term, for use in optimization strategies:application to capillary gas chromatography separation of phenols. Journal of Chromatography A, 1996, 755(2): 235-243
[119] Vanbel P F. Development of flexible and efficient strategies for optimizing chromatographic separations. Journal of Pharmaceutical and Biomedical Analysis, 1999, 21(3): 603-610
[120] Siouffi A M, Phan-Tan-Luu R. Optimization methods in chromatography and capillary electrophoresis. Journal of Chromatography A, 2000, 892(1-2): 75-106
[121] Sivakumar T, Manavalan R, Muralidharan C, et al. Multi-criteria decision making approach and experimental design as chemometric tools to optimize HPLC separationof domperidone and pantoprazole. Journal of Pharmaceutical and Biomedical Analysis, 2007, 43(5): 1842-1848
[122] Schoenmakers P J. Optimization of chromatographic selectivity. Amsterdam: Elsevier, 1986:1-5
[123] Xu Q S, Liang Y Z. Monte Carlo cross validation. Chemometrics and Intelligent Laboratory Systems, 2001, 56(1):1-11
[124] Gourvénec S, Pierna J A F, Massart D L. An evaluation of the PoLiSh smoothedregression and the Monte Carlo cross-validation for the determination of the complexity of a PLS model. Chemometrics and Intelligent Laboratory Systems, 2003, 68(1-2):41-51
[125] Gy P. Sampling for analytical purposes. New York: John Wiley & Sons, 1998: 1-10
[126] Petersen L, Minkkinen P, Esbensen K H. Representative sampling for reliable data analysis: theory of sampling. Chemometrics and Intelligent Laboratory Systems, 2005, 77(1-2): 261-277
[127] Worsfold P J, Gimbert L J, Mankasingh U, et al. Sampling, sample treatment and quality assurance issues for the determination of phosphorus species in natural waters and soils. Talanta, 2005, 66(2): 273-293
[128] Mark H. Comparative study of calibration methods for near-infrared reflectance analysis using a nested experimental design. Analytical Chemistry, 1986, 58(13): 2814-2819
[129] Devos O, Fanget B, Saber A I, et al. Use of a Plackett-Burman design with multivariate calibration for the analysis of polycyclic aromatic hydrocarbons in micellar media by synchronous fluorescence. Analytical Chemistry, 2002, 74(3): 678-683
[130] Borggaard C, Thodberg H H. Optimal minimal neural interpretation of spectra. Analytical Chemistry, 1992, 64(5): 545-551
[131] Wentzell P D, Andrews D T, Walsh J M, et al. Estimation of hydrocarbon types in light gas oils and diesel fuels by ultraviolet absorption spectroscopy and multivariate calibration. Canadian Journal of Chemistry, 1999, 77(3): 391-400
[132] Pedersen D K, Martens H, Nielsen J P, et al. Near-infrared absorption and scattering separated by extended inverted signal correction (EISC): analysis of near-infrared transmittance spectra of single wheat seeds. Applied Spectroscopy, 2002, 56(9): 1206-1214
[133] Lin J, Lo S C, Brown C W. Calibration transfer from a scanning near-IR spectrophotometer to a FT-near-IR spectrophotometer. Analytica Chimica Acta, 1997, 349(1-3): 263-269
[134] Swierenga W, Haanstra W G, De Weijer A P, et al. Comparison of two different approaches toward model transferability in NIR spectroscopy. Applied Spectroscopy, 1998, 52(1): 7-16
[135] Lin J. Near-IR calibration transfer between different temperatures. Applied Spectroscopy, 1998, 52(12): 1591-1596
[136] Wülfert F, Kok W T, de Noord O E, et al. Correction of temperature-induced spectral variation by continuous piecewise direct standardization. Analytical Chemistry, 2000, 72(7): 1639-1644
[137] Koehler F W, Small G W, Combs R J, et al. Calibration transfer algorithm for automated qualitative analysis by passive fourier transform infrared spectrometry. Analytical Chemistry, 2000, 72(7): 1690-1698
[138] Walczak B, Bouveresse E, Massar D L. Standardization of near-infrared spectra in the wavelet domain. Chemometrics and Intelligent Laboratory Systems, 1997, 36(1): 41-51
[139] Blanco M, Coello J, Iturriaga H, et al. Effect of data preprocessing methods in near-infrared diffuse reflectance spectroscopy for the determination of the active compound in a pharmaceutical preparation. Applied Spectroscopy, 1997, 51(2): 240-246
[140] Derringer G,Suich R. Simultaneous optimization of several response variables. Journal of Quality Technology, 1980, 12(4): 214-219
[141] Liang Y Z, Xie P S, Chan K. Quality control of herbal medicines. Journal of Chromatography B, 2004, 812(1-2): 53-70
[142] de Juan A, Tauler R. Chemometrics applied to unravel multicomponent processes and mixtures Revisiting latest trends in multivariate resolution. Analytica Chimica Acta, 2003, 500(1-2): 195-210
[143] Jiang J H, Liang Y Z, Ozaki Y. Principles and methodologies in self-modeling curve resolution. Chemometrics and Intelligent Laboratory Systems, 2004, 71(1): 1-12
[144] de Juan A, Tauler R. Factor analysis of hyphenated chromatographic data exploration, resolution and quantification of multicomponent systems. Journal of Chromatography A, 2007, 1158(1-2): 184-195
[145] Kvalheim O M, Liang Y Z. Heuristic evolving latent projections: resolving two-way multicomponent data. 1. Selectivity, latent-projective graph, datascope, local rank, and unique resolution. Analytical Chemistry, 1992, 64(8): 936-946
[146] Liang Y Z, Kvalheim O M, Keller H R, et al. Heuristic evolving latent projections: resolving two-way multicomponent data. 2. Detection and resolution of minor constituents. Analytical Chemistry, 1992, 64(8): 946-953
[147] Tauler R, Smilde A, Kowalski B. Selectivity, local rank, three-way data analysis and ambiguity in multivariate curve resolution. Journal of Chemometrics, 1995, 9(1): 31-58
[148] Levina E, Wagaman A S, Callender A F, et al. Estimating the number of purechemical components in a mixture by maximum likelihood. Journal of Chemometrics, 2007, 21(1-2): 24-34
[149] Shen H L, Wang J H, Liang Y Z, et al. Chemical rank estimation by multiresolution analysis for two-way data in the presence of background. Chemometrics and Intelligent Laboratory Systems, 1997, 37( 2): 261-269
[150] Shao X G, Cai W S, Sun P Y. Determination of the component number in overlapping multicomponent chromatogram using wavelet transform. Chemometrics and Intelligent Laboratory Systems, 1998, 43(1-2): 147-155
[151] Malinowski E R. Factor Analysis in Chemistry (third ed.). New York: Wiley, 2002: 73-111
[152] Elbergali A, Nygren J, Kubista M. An automated procedure to predict the number of components in spectroscopic data. Analytica Chimica Acta, 1999, 379(1-2): 143-158
[153] Meloun M, ?apek J, Mik?ík P, et al. Critical comparison of methods predicting the number of components in spectroscopic data. Analytica Chimica Acta, 2000, 423(1): 51-68
[154] Fruchter B. Introduction to Factor Analysis. New York: Van Nostrand, 1954: 1-10
[155] Comrey A L. A First Course in Factor Analysis. Orlando: Academic, 1973: 1-5
[156] Hugus Jr. Z Z, El-Awady A A. The determination of the number of species present in a system: A new matrix rank treatment of spectrophotometric data. Journal of Physical Chemistry, 1971, 75(19): 2954-2957
[157] Ritter G l, Lowry S R, Isenhour T L, et al. Factor analysis of the mass spectra of mixtures. Analytical Chemistry, 1976,48(3): 591-595
[158] Kankare J J. Computation of equilibrium constants for multicomponent systems from spectrophotometric data. Analytical Chemistry, 1970, 42(12): 1322-1326
[159] Wallace R M, Katz S M. A method for the determination of rank in the analysis of absorption spectra of multicomponent systems. Journal of Physical Chemistry, 1964, 68(12): 3890-3892
[160] Kaiser H F. The application of electronic computers to factor analysis. Educational and Psychological Measurement, 1960, 20(1): 141-151
[161] Kindsvanter J H, Weiner P H, Klingen T J. Correlation of retention volumes of substitutued carboranes with molecular properties in high pressure liquid chromatography using factor analysis. Analytical Chemistry, 1974, 46(8): 982-988
[162] Chen Z P, Liang Y Z, Jiang J H, et al. Determination of the number of components in mixtures using a new approach incorporating chemical information. Journal of Chemometrics, 1999, 13(1): 15-30
[163] Silverman B W. Smoothed functional principal components analysis by choice of norm. Annals of Statistics, 1996, 24(1): 1-24
[164] Wang J H, Liang Y Z, Jiang J H, et al. Local chemical rank estimation of two-way data in the presence of heteroscedastic noise: A morphological approach. Chemometrics and Intelligent Laboratory Systems, 1996, 32(2): 265-272
[165] Shen H L, Stordrange L, Manne R, et al. The morphological score and its application to chemical rank determination. Chemometrics and Intelligent Laboratory Systems, 2000, 51(1): 37-47
[166] Cattell R B. Extracting the correct number of factors in factor analysis. Educational and Psychological Measurement, 1958, 18(4): 791-838
[167] Shrager R I, Hendler R W. Titration of individual components in a mixture with resolution of difference spectra, pKs, and redox transitions. Analytical Chemistry, 1982, 54(7): 1147-1152
[168] Rossi T M, Warner I M. Rank estimation of emission excitation matrixes using frequency analysis of eigenvectors. Analytical Chemistry, 1986, 58(4): 810-815
[169] Tu X M, Burdick D S, Millican D W, et al. Canonical correlation technique for rank estimation of excitation-emission matrixes. Analytical Chemistry, 1989, 61(19): 2219-2224
[170] Shen H L, Liang Y Z, Kvalheim O M, et al. Determination of chemical rank of two-way data from mixtures using subspace comparisons. Chemometrics and Intelligent Laboratory Systems, 2000, 51(1): 49-59
[171] Malinowski E R. Determination of the number of factors and the experimental error in a data matrix. Analytical Chemistry, 1977, 49(4): 612-617
[172] Wold S. Cross-validatory estimation of the number of components in factor and principal components models. Technometrics, 1978, 20(4): 397-405
[173] Malinowski E R. Statistical F-tests for abstract factor analysis and target testing. Journal of Chemometrics, 2005, 3(1): 49-60
[174] Faber K, Kowalski B R. Modification of Malinowski's F-test for abstract factor analysis applied to the Quail Roost II data sets. Journal of Chemometrics, 1997, 11( 1): 53-72
[175] Malinowski E R. Abstract factor analysis of data with multiple sources of errorand a modified Faber-Kowalski f-test. Journal of Chemometrics, 1999, 13(2): 69-81
[176] Ohta N. Estimating absorption bands of component dyes by means of principal component analysis. Analytical Chemistry, 1973, 45(3): 553-557
[177] Sharaf M A, Kowalski B R. Quantitative resolution of fused chromatographic peaks in gas chromatography/mass spectrometry. Analytical Chemistry, 1982, 54(8): 1291-1296
[178] Gampp H, Maeder M, Meyer C J, et al. Calculation of equilibrium constants from multiwavelength spectroscopic data—III model-free analysis of spectrophotometric and ESR titrations. Talanta, 1985, 32 (12): 1133-1139
[179] Maeder M. Evolving factor analysis for the resolution of overlapping chromatographic peaks. Analytical Chemistry, 1987, 59(3): 527-530
[180] Keller H R, Massart D L. Peak purity control in liquid chromatography with photodiode-array detection by a fixed size moving window evolving factor analysis. Analytica Chimica Acta, 1991, 246(2): 379-390
[181] Ritter C, Gilliard J A, Cumps J, et al. Corrections for heteroscedasticity in window evolving factor analysis. Analytica Chimica Acta, 1996, 318(2): 125-136
[182] Alsberg B K. Properties of local rank map vectors from multidetection chromatograms. Analytica Chimica Acta, 1996, 318(2): 137-150
[183] Whitson A C, Maeder M. Exhaustive evolving factor analysis (E-EFA). Journal of Chemometrics, 2001, 15(5): 475-484
[184] Zeng Z D, Xu C J, Liang Y Z, et al. Sectional moving window factor analysis for diagnosing elution chromatographic patterns. Chemometrics and Intelligent Laboratory Systems, 2003, 69(1-2): 89-101
[185] Chen Z P, Morris J, Martin E, et al. Recursive evolving spectral projection for revealing the concentration windows of overlapping peaks in two-way chromatographic experiments. Chemometrics and Intelligent Laboratory Systems, 2004, 72(1): 9-19
[186] Toft J, Kvalheim O M. Eigenstructure tracking analysis for revealing noise pattern and local rank in instrumental profiles: Application to transmittance and absorbance IR spectroscopy. Chemometrics and Intelligent Laboratory Systems, 1993, 19(1): 65-73
[187] Sánchez F C, Van Den Bogaert B, Rutan S C, et al. Multivariate peak purity approaches. Chemometrics and Intelligent Laboratory Systems, 1996, 34(2):139-171
[188] Rodríguez-Cuesta M J, BoquéR, Rius F X, et al. Development and validation of a method for determining pesticides in groundwater from complex overlapped HPLC signals and multivariate curve resolution. Chemometrics and Intelligent Laboratory Systems,2005, 77(1-2): 251-260
[189] Windig W, Guilment J. Interactive self-modeling mixture analysis. Analytical Chemistry, 1991, 63(14): 1425-1432
[190] Windig W, Heckler C E. Self-modeling mixture analysis of categorized pyrolysis mass spectral data with the SIMPLISMA approach. Chemometrics and Intelligent Laboratory Systems, 1992, 14(1-3): 195-207
[191] Sánchez F C, Massart D L. Application of SIMPLISMA for the assessment of peak purity in liquid chromatography with diode array detection. Analytica Chimica Acta, 1994, 298(3): 331-339
[192] Sánchez FC, Toft J, Van Den Bogaert B, et al. Orthogonal projection approach applied to peak purity assessment. Analytical Chemistry, 1996, 68 (1): 79-85
[193] Gemperline P J. A priori estimates of the elution profiles of the pure components in overlapped liquid chromatography peaks using target factor analysis. Journal of Chemical Information and Computer Sciences, 1984, 24(4): 206 - 212
[194] Fabre H, Le Bris A, Blanchin M D. Evaluation of different techniques for peak purity assessment on a diode-array detector in liquid chromatography. Journal of Chromatography A, 1995, 697(1-2): 81-88
[195] Bylund D, Danielsson R, Markides K E. Peak purity assessment in liquid chromatography-mass spectrometry. Journal of Chromatography A, 2001, 915(1-2): 43-52
[196] Arvis T D, Kalivas J H. Fundamentals of condition index evolving profiles for qualitative analysis of unresolved chromatographic peaks. Analytica Chimica Acta, 1992, 266(1): 13-24
[197] Bakken G A, Kalivas J H. Assessing chromatographic peak purity using condition index and singular value evolving profiles. Analytica Chimica Acta, 1995, 300(1-3): 173-181
[198] Vanslyke S J, Wentzell P D. Real-time principal component analysis using parallel Kalman filter networks for peak purity analysis. Analytical Chemistry, 1991, 63(21): 2512-2519
[199] Hopke P K, Alpert D J, Roscoe B A. Fantasia-a program for target transformation factor analysis to apportion sources in environmental samples.Computers and Chemistry, 1983, 7(3): 149-155
[200] Vandeginste B G M, Derks W, Kateman G. Multicomponent self-modelling curve resolution in high-performance liquid chromatography by iterative target transformation analysis. Analytica Chimica Acta, 1985, 173: 253-264
[201] De Juan A, Van Den Bogaert B, Sánchez F C, et al. Application of the needle algorithm for exploratory analysis and resolution of HPLC-DAD data. Chemometrics and Intelligent Laboratory Systems, 1996, 33(2): 133-145
[202] Xie Y L, Baeza-Baeza J J, Ramis-Ramos G. Assessment of peak purity in liquid chromatography using condition index and singular value evolving profiles. Analytica Chimica Acta, 1995, 317(1-3): 17-32
[203] Wiberg K, Andersson M, Hagman A, et al. Peak purity determination with principal component analysis of high-performance liquid chromatography-diode array detection data. Journal of Chromatography A, 2004, 1029(1-2): 13-20
[204] Polster J, Sauerwald N, Feucht W, et al. New methods for spectrometric peak purity analysis in chromatography. Journal of Chromatography A, 1998, 800(2): 121-133
[205] Gilliard J A, Ritter C. Use of simulated liquid chromatography-diode array detection data for the definition of a guide curve in peak purity assessment by spectral comparison. Journal of Chromatography A, 1997,786(1): 1-11
[206] Gong F, Liang Y Z, Xu Q S, et al. Evaluation of separation quality in two-dimensional hyphenated chromatography. Analytica Chimica Acta, 2001, 450(1-2): 99-114
[207] Malinowski E R. Obtaining the key set of typical vectors by factor analysis and subsequent isolation of component spectra. Analytica Chimica Acta, 1982, 134: 129-137
[208] Faber K, Lorber A, Kowalski B R. Analytical figures of merit for tensorial calibration. Journal of Chemometrics, 1997, 11(5): 419-461
[209] Messick N J, Kalivas J H, Lang P M. Selectivity and related measures for nth-order data. Analytical Chemistry, 1996, 68(9): 1572-1579
[210] Vivó-Truyols G, Torres-LapasióJ R, García-Alvarez-Coque M C. Net analyte signal as a deconvolution-oriented resolution criterion in the optimisation of chromatographic techniques. Journal of Chromatography A, 2003, 991(1): 47-59
[211] Faber N M. Exact presentation of multivariate calibration model as univariate calibration graph. Chemometrics and Intelligent Laboratory Systems, 2000,50(1): 107-114
[212] Duewer D L, Kowalski B R, Fasching J L. Improving the reliability of factor analysis of chemical data by utilizing the measured analytical uncertainty. Analytical Chemistry, 1976, 48(13): 2002-2010
[213] Daszykowski M, Walczak B. Use and abuse of chemometrics in chromatography. Trends in Analytical Chemistry, 2006, 25(11): 1081-1096