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Affine combination-based over-sampling for imbalanced regression 基于仿射组合的不平衡回归过度采样
IF 2.4 4区 化学 Q1 Mathematics Pub Date : 2024-02-09 DOI: 10.1002/cem.3537
Zhen-Zhen Li, Niu Huang, Lun-Zhao Yi, Guang-Hui Fu

Imbalanced domain prediction analysis is currently one of the hot research topics. Many real-world data mining analyses involve using imbalanced data to obtain predictive models. In the context of imbalance, research on classification problems has been extensive, but research on regression problems is negligible. Rare values rarely occur in imbalanced regression problems, but the focus is on accurately predicting the continuous target variables of rare instances. One of the challenges in imbalanced regression is finding a suitable strategy to rebalance the original dataset in order to improve the predictive performance of the model in rare instances. In this study, two algorithms are proposed: sigma nearest over-sampling based on convex combination for regression (SNOCCR) and affine combination-based over-sampling (ACOS). ACOS rebalances the original dataset by generating new instances through the affine combinations of the original examples. The region where the new instances are generated can be adjusted based on the distribution of the data, ensuring that the generated cases better mimic the distribution of the original examples. The comparison among ACOS, SNOCCR, and other preprocessing methods was conducted on 15 datasets to validate the predictive performance of models trained on rebalanced datasets for rare instances. The experimental results indicate that ACOS outperforms other existing methods.

不平衡域预测分析是当前的热门研究课题之一。现实世界中的许多数据挖掘分析都涉及使用不平衡数据来获得预测模型。在不平衡的背景下,分类问题的研究已经非常广泛,但回归问题的研究却微乎其微。稀有值很少出现在不平衡回归问题中,但重点是准确预测稀有实例的连续目标变量。不平衡回归的挑战之一是找到一种合适的策略来重新平衡原始数据集,以提高模型在罕见实例中的预测性能。本研究提出了两种算法:基于回归凸组合的 sigma nearest 过度采样(SNOCCR)和基于仿射组合的过度采样(ACOS)。ACOS 通过原始实例的仿射组合生成新实例,从而重新平衡原始数据集。生成新实例的区域可根据数据的分布进行调整,确保生成的实例能更好地模仿原始实例的分布。在 15 个数据集上对 ACOS、SNOCCR 和其他预处理方法进行了比较,以验证在重新平衡数据集上训练的模型对罕见实例的预测性能。实验结果表明,ACOS 优于其他现有方法。
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引用次数: 0
Two new methods for the estimation and interpretation of the range of feasible profiles in multivariate curve resolution and their implications to analytical chemistry 在多元曲线解析中估算和解释可行剖面范围的两种新方法及其对分析化学的影响
IF 2.4 4区 化学 Q1 Mathematics Pub Date : 2024-01-30 DOI: 10.1002/cem.3535
Alejandro C. Olivieri

Two new models have been recently introduced for studying the remaining rotational ambiguity in the bilinear decomposition of matrix data. One of the models is N-BANDS, which yields two extreme profiles per sample component, corresponding to maximum or minimum signal contribution function or relative component area under its concentration profile. It is highly useful for computing the relative root mean square error due to rotational ambiguity in estimated analyte concentrations (RMSERA), which numerically quantifies the impact of the phenomenon in terms of prediction uncertainty. Since N-BANDS successfully consider the presence of instrumental noise in the data, it is extremely useful for the analysis of real data sets. The other model is SW-N-BANDS, which is similar to N-BANDS, but is applied in a sensor wise manner, that is, computing the maximum and minimum intensity value at each sensor. It provides the boundaries of the full set of feasible profiles, and helps to better understand the behavior of a given component under the application of several constraints. Both models are described in light of both simulations and experimental data, illustrating their main characteristics of importance to analytical chemistry studies.

最近推出了两个新模型,用于研究矩阵数据双线性分解中剩余的旋转模糊性。其中一个模型是 N-BANDS,它能为每个样本组分生成两个极端剖面,分别对应于最大或最小信号贡献函数或浓度剖面下的相对组分面积。它非常适用于计算由于估计分析物浓度旋转模糊性而导致的相对均方根误差(RMSERA),该误差可从预测不确定性的角度对该现象的影响进行数值量化。由于 N-BANDS 成功地考虑到了数据中存在的仪器噪声,因此对实际数据集的分析非常有用。另一种模型是 SW-N-BANDS,它与 N-BANDS 相似,但以传感器为单位应用,即计算每个传感器的最大和最小强度值。它提供了全套可行剖面的边界,有助于更好地理解特定组件在多个约束条件下的行为。这两种模型都根据模拟和实验数据进行了描述,说明了它们在分析化学研究中的主要特性。
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引用次数: 0
Quantitative study on impact damage of honey peaches based on reflection, absorbance, and Kubelka-Munk spectrum combined with color characteristics 基于反射率、吸光度、库贝尔卡-蒙克光谱与颜色特征相结合的蜜桃撞击损伤定量研究
IF 2.4 4区 化学 Q1 Mathematics Pub Date : 2024-01-20 DOI: 10.1002/cem.3532
Bin Li, Jiping Zou, Chengtao Su, Feng Zhang, Yande Liu, Jian Wu, Nan Chen, Yihua Xiao

Impact damage is one of the key factors affecting the quality of honey peaches. Quantitative study of impact damage is of great significance for the sorting of postharvest quality of honey peaches. In order to realize the quantitative prediction of impact damage of honey peaches, the impact damage of honey peaches was quantitatively studied based on the fusion of color characteristics with reflection spectra (R), absorbance spectra (A), and Kubelka-Munk spectra (K-M). The mechanical parameters of honey peaches during collision were obtained using a single pendulum collision device. Reflectance spectra and color characteristics of damaged honey peaches were obtained by a hyperspectral imaging system. The R spectra were converted into A and K-M spectra, and the partial least squares regression (PLSR) model was built based on the three spectra and the three spectra combined with color characteristics for quantitative prediction of mechanical parameters. The results show that the prediction performance of the PLSR model is improved by combining color features with spectral information. In order to eliminate the redundant information in the spectral data, the competitive adaptive reweighted sampling (CARS) algorithm was used to select the characteristic wavelengths of the three spectra, and the selected characteristic wavelengths were fused with the color features to establish the PLSR model. The results show that the PLSR model built by the characteristic wavelengths of the A spectrum combined with the color features has the best prediction performance for the mechanical parameters. The RP value for maximum force is 0.862, and the RP value for damage depth is 0.894. The results of this study not only provide the theoretical support for the quality sorting, packaging, and transportation of honey peaches but also provide the reference for the biomechanical properties of various agricultural products.

冲击损伤是影响蜜桃质量的关键因素之一。冲击损伤的定量研究对于蜜桃采后品质的分选具有重要意义。为了实现蜜桃撞击损伤的定量预测,基于颜色特征与反射光谱(R)、吸光度光谱(A)和库贝尔卡-蒙克光谱(K-M)的融合,对蜜桃的撞击损伤进行了定量研究。使用单摆碰撞装置获得了蜜桃在碰撞过程中的机械参数。利用高光谱成像系统获得了受损蜜桃的反射光谱和颜色特征。将 R 光谱转换为 A 光谱和 K-M 光谱,并根据三条光谱和三条光谱结合颜色特征建立偏最小二乘回归(PLSR)模型,对力学参数进行定量预测。结果表明,将颜色特征与光谱信息相结合可提高 PLSR 模型的预测性能。为了消除光谱数据中的冗余信息,采用竞争性自适应加权采样(CARS)算法来选择三条光谱的特征波长,并将所选的特征波长与颜色特征融合建立 PLSR 模型。结果表明,由 A 光谱特征波与颜色特征相结合建立的 PLSR 模型对力学参数的预测性能最佳。最大力的 RP 值为 0.862,损坏深度的 RP 值为 0.894。该研究结果不仅为蜜桃的质量分拣、包装和运输提供了理论支持,也为各种农产品的生物力学特性提供了参考。
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引用次数: 0
Assessment of adulteration of sage (Salvia sp.) with olive leaves using high-performance thin-layer chromatography, image analysis, and multivariate linear modeling 利用高效薄层色谱法、图像分析和多元线性模型评估鼠尾草(丹参)与橄榄叶的掺假情况
IF 2.4 4区 化学 Q1 Mathematics Pub Date : 2024-01-20 DOI: 10.1002/cem.3533
Nina Tomčić, Milica Jankov, Petar Ristivojević, Jelena Trifković, Filip Andrić

According to the study carried out at the University of Bristol, 60% of oregano spices present on the European Union (EU) market are adulterated with olive, myrtle, cistus, and hazelnut leaves. According to the same authors, the sage products are adulterated by similar bulking agents. The aim of this study was to assess possibilities for detection of sage adulteration by olive leaves using high-performance thin-layer chromatography (HPTLC) coupled with digital image analysis and multivariate linear regression/classification (partial least squares and partial least squares discriminant analysis). Twenty-four samples (4 pure sage leaves, 4 pure olive leaves, and 16 mixtures of olive and sage leaves with content of added olive leaves varying in 5%, 10%, 20%, and 50%) have been prepared, extracted, and analyzed under normal-phase conditions. Several derivatization methods were tested, and derivatized HPTLC plates were inspected under visible or ultraviolet light. Digital images of chromatograms were recorded. In order to minimize effects of intraplate and interplate peak shifts, background changes, and baseline drifts, correlation-optimized warping, standard normal variate, and mean centering were applied to acquired signals. Partial least squares and partial least squares discriminant analysis models with moderate complexity (two to four latent variables) based on chromatographic signals obtained after derivatization by FeCl3, anisaldehyde–sulfuric acid, and 2,2-diphenyl-1-picrylhydrazyl demonstrated good statistical performances with R2 ranging 0.894–0.998 and relative prediction error of 4–12%. Misclassification error <4% was obtained in the case of 2,2-diphenyl-1-picrylhydrazyl and anisaldehyde–sulfuric acid derivatization. Therefore, HPTLC combined with multivariate image analysis, signal processing, and linear modeling proved to be promising, cost-effective chromatographic tool for assessment of sage adulteration by olive leaves.

根据布里斯托尔大学进行的研究,欧盟市场上 60% 的牛至香料掺杂了橄榄叶、桃金娘叶、肉苁蓉叶和榛子叶。据同一作者称,鼠尾草产品也掺杂了类似的膨松剂。本研究的目的是评估使用高效薄层色谱法(HPTLC)结合数字图像分析和多元线性回归/分类法(偏最小二乘法和偏最小二乘法判别分析)检测橄榄叶掺假鼠尾草的可能性。在正相条件下制备、提取和分析了 24 种样品(4 种纯鼠尾草叶、4 种纯橄榄叶、16 种橄榄叶和鼠尾草叶混合物,其中橄榄叶的添加量分别为 5%、10%、20% 和 50%)。对几种衍生方法进行了测试,并在可见光或紫外光下对衍生后的 HPTLC 板进行了检测。记录色谱图的数字图像。为了尽量减少板内和板间峰移、背景变化和基线漂移的影响,对获取的信号进行了相关优化翘曲、标准正态变异和平均居中处理。基于氯化铁、苯甲醛-硫酸和 2,2-二苯基-1-苦基肼衍生后获得的色谱信号建立的部分最小二乘法和部分最小二乘法判别分析模型具有中等复杂度(2 至 4 个潜变量),显示出良好的统计性能,R2 为 0.894-0.998,相对预测误差为 4-12%。2,2-二苯基-1-苦基肼和苯甲醛-硫酸衍生化的分类误差为 4%。因此,HPTLC 与多元图像分析、信号处理和线性建模相结合,被证明是评估橄榄叶中鼠尾草掺假情况的一种前景广阔、经济高效的色谱工具。
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引用次数: 0
Adaptive deep fusion neural network based soft sensor for industrial process 基于自适应深度融合神经网络的工业过程软传感器
IF 2.4 4区 化学 Q1 Mathematics Pub Date : 2024-01-20 DOI: 10.1002/cem.3529
Xiaoping Guo, Jialin Chong, Yuan Li

Deep neural networks have become an important tool for soft sensor modeling. However, common deep autoencoder networks are limited to mining the effective information of each input layer during hierarchical training, ignoring the loss of effective information in the original input data and accumulating it layer-by-layer, resulting in incomplete feature representation of the original input. At the same time, there is a lack of mining for temporal correlation between process samples and an adaptive mechanism to strengthen temporal related features, resulting in insufficient process information mining. In addition, deep neural networks generally have overfitting problems. To this end, an adaptive deep fusion neural network (ADFNN) method is proposed. This method reconstructs the original input data at each layer of the feature extraction network. By using the reconstructed original input error in pre-training loss, it reduces the loss of effective information from the original input. Simultaneously, incorporating sliding windows and self-attention mechanisms to select and calculate the contribution of historical samples to the current sample, integrating temporal related information, and overcoming dependence on high-dimensional local features by minimizing Kullback-Leibier (KL) divergence penalty terms. Finally, the temporal features are adaptively weighted and connected to a fully connected network to achieve quality prediction. Simulation experiments were conducted in cases of debutanizer and industrial polyethylene production to verify the effectiveness of the proposed method. The experimental results show that compared to the stacked autoencoder (SAE), target dependent stacked autoencoder (TSAE), and stacked isomorphic autoencoder (SIAE) models, the proposed method ADFNN has improved prediction accuracy by 2.4%, 1.7%, and 0.5% in the case of a debutanizer, respectively. In the industrial polyethylene production case, it has increased by 3.6%, 3.3%, and 1.8%, respectively.

深度神经网络已成为软传感器建模的重要工具。然而,常见的深度自动编码器网络仅限于在分层训练过程中挖掘各输入层的有效信息,忽略了原始输入数据中有效信息的丢失,逐层积累,导致原始输入的特征表示不完整。同时,缺乏对过程样本间时间相关性的挖掘和强化时间相关特征的自适应机制,导致过程信息挖掘不够充分。此外,深度神经网络普遍存在过拟合问题。为此,我们提出了一种自适应深度融合神经网络(ADFNN)方法。该方法会在特征提取网络的每一层重建原始输入数据。通过在预训练损失中使用重建的原始输入误差,可以减少原始输入的有效信息损失。同时,结合滑动窗口和自我关注机制来选择和计算历史样本对当前样本的贡献,整合与时间相关的信息,并通过最小化 Kullback-Leibier (KL) 发散惩罚项来克服对高维局部特征的依赖。最后,对时间特征进行自适应加权,并将其连接到全连接网络,以实现高质量预测。为了验证所提方法的有效性,我们在脱utanizer 和工业聚乙烯生产中进行了模拟实验。实验结果表明,与堆叠式自动编码器(SAE)、目标依赖堆叠式自动编码器(TSAE)和堆叠式同构自动编码器(SIAE)模型相比,所提出的 ADFNN 方法在去氨酸装置中的预测精度分别提高了 2.4%、1.7% 和 0.5%。在工业聚乙烯生产案例中,预测准确率分别提高了 3.6%、3.3% 和 1.8%。
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引用次数: 0
Implications of confounding from unmodeled interactions between explanatory variables when using latent variable regression models to make inferences 使用潜变量回归模型进行推理时,解释变量之间未建模的相互作用所产生的混淆影响
IF 2.4 4区 化学 Q1 Mathematics Pub Date : 2024-01-12 DOI: 10.1002/cem.3531
Olav M. Kvalheim, Warren S. Vidar, Tim U. H. Baumeister, Roger G. Linington, Nadja B. Cech

With linear dependency between the explanatory variables, partial least squares (PLS) regression is commonly used for regression analysis. If the response variable correlates to a high degree with the explanatory variables, a model with excellent predictive ability can usually be obtained. Ranking of variable importance is commonly used to interpret the model and sometimes this interpretation guides further experimentation. For instance, when analyzing natural product extracts for bioactivity, an underlying assumption is that the highest ranked compounds represent the best candidates for isolation and further testing. A problem with this approach is that in most cases, the number of compounds is larger than the number of samples (and usually much larger) and that the concentrations of the compounds correlate. Furthermore, compounds may interact as synergists or as antagonists. If the modeling process does not account for this possibility, the interpretation can be thoroughly wrong because unmodeled variables that strongly influence the response will give rise to confounding of a first-order PLS model and send the experimenter on a wrong track. We show the consequences of this by a practical example from natural product research. Furthermore, we show that by including the possibility of interactions between explanatory variables, visualization using a selectivity ratio plot may provide model interpretation that can be used to make inferences.

在解释变量之间存在线性依赖关系的情况下,偏最小二乘法(PLS)回归通常用于回归分析。如果响应变量与解释变量高度相关,通常可以得到一个预测能力极强的模型。变量重要性的排序通常用于解释模型,有时这种解释会指导进一步的实验。例如,在分析天然产品提取物的生物活性时,一个基本假设是排名最靠前的化合物是分离和进一步测试的最佳候选化合物。这种方法存在的一个问题是,在大多数情况下,化合物的数量比样本的数量要多(通常要多得多),而且化合物的浓度是相关的。此外,化合物之间可能存在协同作用或拮抗作用。如果建模过程没有考虑到这种可能性,解释就会完全错误,因为对反应有强烈影响的未建模变量会对一阶 PLS 模型造成混淆,从而使实验者走上错误的道路。我们通过一个天然产品研究的实际例子来说明这种情况的后果。此外,我们还表明,通过纳入解释变量之间相互作用的可能性,使用选择性比值图进行可视化可以提供模型解释,并可用于推论。
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引用次数: 0
The difference of model robustness assessment using cross-validation and bootstrap methods 使用交叉验证法和引导法评估模型稳健性的区别
IF 2.4 4区 化学 Q1 Mathematics Pub Date : 2024-01-11 DOI: 10.1002/cem.3530
Rita Lasfar, Gergely Tóth

The validation principles on Quantitative Structure Activity Relationship issued by Organization for Economic and Co-operation and Development describe three criteria of model assessment: goodness of fit, robustness and prediction. In the case of robustness, two ways are possible as internal validation: bootstrap and cross-validation. We compared these validation metrics by checking their sample size dependence, rank correlations to other metrics and uncertainty. We used modeling methods from multivariate linear regression to artificial neural network on 14 open access datasets. We found that the metrics provide similar sample size dependence and correlation to other validation parameters. The individual uncertainty originating from the calculation recipes of the metrics is much smaller for both ways than the part caused by the selection of the training set or the training/test split. We concluded that the metrics of the two techniques are interchangeable, but the interpretation of cross-validation parameters is easier according to their similar range to goodness-of-fit and prediction metrics. Furthermore, the variance originating from the random elements of the calculation of cross-validation metrics is slightly smaller than those of bootstrap ones, if equal calculation load is applied.

经济合作与发展组织发布的《定量结构活动关系验证原则》描述了模型评估的三个标准:拟合度、稳健性和预测。在稳健性方面,有两种内部验证方法:自举法和交叉验证。我们通过检查这些验证指标的样本量依赖性、与其他指标的等级相关性和不确定性,对它们进行了比较。我们在 14 个开放数据集上使用了从多元线性回归到人工神经网络的建模方法。我们发现,这些指标提供了类似的样本大小依赖性以及与其他验证参数的相关性。在这两种方法中,源于度量标准计算配方的个别不确定性要比源于训练集选择或训练/测试分割的部分小得多。我们的结论是,这两种技术的度量标准可以互换,但交叉验证参数的解释更容易,因为它们与拟合优度和预测度量标准的范围相似。此外,在计算负荷相同的情况下,交叉验证指标计算中随机因素产生的方差略小于 bootstrap 指标。
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引用次数: 0
Sample selection method using near-infrared spectral information entropy as similarity criterion for constructing and updating peach firmness and soluble solids content prediction models 利用近红外光谱信息熵作为相似性标准的样本选择方法,用于构建和更新桃子硬度和可溶性固形物含量预测模型
IF 2.4 4区 化学 Q1 Mathematics Pub Date : 2023-12-19 DOI: 10.1002/cem.3528
Yande Liu, Cong He, Xiaogang Jiang

When using near-infrared (NIR) techniques for analysis, model construction and maintenance updates are essential. When model construction is performed in machine learning, the sample set is usually divided into the calibration set and the validation set. The representativeness of the calibration set and the reasonable distribution of the validation set affects the accuracy of the established model. In addition, when maintaining and updating models, selecting the most informative updated sample not only improves the model prediction accuracy but also reduces sample preparation. In this paper, the spectral information entropy (SIE) is proposed to be used as a similarity criterion for dividing the sample set and use this criterion to select updated samples. The Kennard–Stone (KS) and the sample set portioning based on joint xy distance (SPXY) methods were used for comparison to verify the superiority of the proposed method. The results showed that the model built after dividing the sample set using the SIE method has good prediction effect compared with KS and SPXY method. When predicting soluble solid content (SSC) and hardness, the prediction determination coefficient (RP2) was improved by more than 15%, and the root mean square error (RMSE) of prediction was reduced by 50%. In terms of model updating, selecting a small number of updated samples using the SIE method can improve the correlation coefficient (RP) to more than 80%, and updated models' prediction accuracy is higher than that of KS and SPXY method. It is confirmed that the SIE method can make the NIR analysis technique more reliable.

使用近红外(NIR)技术进行分析时,模型构建和维护更新至关重要。在机器学习中构建模型时,样本集通常分为校准集和验证集。校准集的代表性和验证集的合理分布会影响所建模型的准确性。此外,在维护和更新模型时,选择信息量最大的更新样本不仅能提高模型预测精度,还能减少样本准备工作。本文提出将光谱信息熵(SIE)作为划分样本集的相似性准则,并利用该准则选择更新样本。比较了 Kennard-Stone (KS) 方法和基于联合 x-y 距离 (SPXY) 的样本集划分方法,以验证所提方法的优越性。结果表明,与 KS 和 SPXY 方法相比,使用 SIE 方法分割样品集后建立的模型具有良好的预测效果。在预测可溶性固形物含量(SSC)和硬度时,预测判定系数(RP2$$ {R}_P^2 $$)提高了 15%以上,预测均方根误差(RMSE)降低了 50%。在模型更新方面,利用 SIE 方法选择少量更新样本可以将相关系数(RP$$ {R}_P $$)提高到 80% 以上,更新后模型的预测精度高于 KS 和 SPXY 方法。因此,SIE 方法可以使近红外分析技术更加可靠。
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引用次数: 0
Iterative re-weighted multilinear partial least squares modelling for robust predictive modelling 鲁棒预测模型的迭代重加权多元线性偏最小二乘建模
IF 2.4 4区 化学 Q1 Mathematics Pub Date : 2023-12-06 DOI: 10.1002/cem.3527
Puneet Mishra, Kristian Hovde Liland

Higher order data are commonly encountered in the domain of chemometrics, often generated by advanced analytical instruments. Due to the multilinear nature of the data, higher order data require different regression approaches compared with traditional two-way data for predictive modelling. The main aim is usually to extract the rich multilinear information, which is often lost if the data are simply analysed in unfolded form. A common algorithm for multilinear predictive modelling is N-way partial least squares (NPLS). However, a limitation of NPLS is that it inherently does not handle outlying observations, which can be detrimental to the model. This work presents a new robust multilinear predictive modelling approach based on iterative down-weighting of the outlier observations in both predictor and response space. A key benefit of the method is that it only requires a single extra parameter to tune. In this work, the algorithm is described, and the method is demonstrated on three real multilinear data sets. In all cases, the presented method outperformed the traditional NPLS modelling regarding the root mean squared error of prediction.

高阶数据通常在化学计量学领域中遇到,通常由先进的分析仪器产生。由于数据的多线性性质,与传统的双向数据相比,高阶数据需要不同的回归方法来进行预测建模。主要目的通常是提取丰富的多线性信息,如果简单地以展开形式分析数据,这些信息往往会丢失。多线性预测建模的常用算法是n向偏最小二乘法。然而,不良贷款的一个限制是它本质上不处理外围观测,这可能对模型有害。这项工作提出了一种新的鲁棒多线性预测建模方法,该方法基于预测和响应空间中离群值观测的迭代降权。该方法的一个关键优点是,它只需要一个额外的参数即可进行调优。本文对该算法进行了描述,并在三个真实的多线性数据集上进行了验证。在所有情况下,所提出的方法在预测均方根误差方面优于传统的不良贷款建模。
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引用次数: 0
Correction to “A novel eco-friendly methods for simultaneous determination of aspirin, clopidogrel, and atorvastatin or rosuvastatin in their fixed-dose combination using chemometric techniques and artificial neural networks” 更正“利用化学计量技术和人工神经网络同时测定阿司匹林、氯吡格雷和阿托伐他汀或瑞舒伐他汀固定剂量组合的新型环保方法”
IF 2.4 4区 化学 Q1 Mathematics Pub Date : 2023-11-14 DOI: 10.1002/cem.3526

AlSawy NS, ElKady EF, Mostafa EA. A novel eco-friendly methods for simultaneous determination of aspirin, clopidogrel, and atorvastatin or rosuvastatin in their fixed-dose combination using chemometric techniques and artificial neural networks. Journal of Chemometrics. 2023;37(5):e3474. doi:10.1002/cem.3474

The first letter ‘A’ in the article title was mistakenly added. The updated article title is below.

“Novel eco-friendly methods for simultaneous determination of aspirin, clopidogrel, and atorvastatin or rosuvastatin in their fixed-dose combination using chemometric techniques and artificial neural networks”

We apologize for this error.

AlSawy NS, ElKady EF, Mostafa EA.利用化学计量技术和人工神经网络同时测定阿司匹林、氯吡格雷和阿托伐他汀或瑞舒伐他汀固定剂量组合的环保新方法。化学计量学学报,2009;37(5):1145 - 1145。doi: 10.1002 /杰姆。文章标题中的第一个字母“A”加错了。更新后的文章标题如下。“使用化学计量学技术和人工神经网络同时测定阿司匹林、氯吡格雷和阿托伐他汀或瑞舒伐他汀固定剂量组合的新型环保方法”我们为这个错误道歉。
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Journal of Chemometrics
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