Partial least squares for discrimination in fMRI data

Multivariate methods for discrimination were used in the comparison of brain activation patterns between groups of cognitively normal women who are at either high or low Alzheimer's disease risk based on family history and apolipoprotein-E4 status. Linear discriminant analysis (LDA) was preceded by dimension reduction using principal component analysis (PCA), partial least squares (PLS) or a new oriented partial least squares (OrPLS) method. The aim was to identify a spatial pattern of functionally connected brain regions that was differentially expressed by the risk groups and yielded optimal classification accuracy. Multivariate dimension reduction is required prior to LDA when the data contain more feature variables than there are observations on individual subjects. Whereas PCA has been commonly used to identify covariance patterns in neuroimaging data, this approach only identifies gross variability and is not capable of distinguishing among-groups from within-groups variability. PLS and OrPLS provide a more focused dimension reduction by incorporating information on class structure and therefore lead to more parsimonious models for discrimination. Performance was evaluated in terms of the cross-validated misclassification rates. The results support the potential of using functional magnetic resonance imaging as an imaging biomarker or diagnostic tool to discriminate individuals with disease or high risk.     

激光诱导击穿光谱结合偏最小二乘法定量分析脐橙中Cd含量

基于激光诱导击穿光谱(LIBS)技术对赣南脐橙中Cd元素进行定量分析. 利用LIBS获取样品中Cd元素的特征谱线信息, 并结合原子吸收分光光度计测量样品中Cd元素的真实含量.采用五点平滑法和中心化法对样品光谱数据进行预处理, 基于偏最小二乘法(PLS)对其中的39个样品建立Cd元素的定量分析模型, 在该模型的基础上预测另外13个样品的Cd含量, 并对PLS模型进行对比验证. PLS模型中拟合曲线的相关系数为0.9806, 12个样品的验证结果的相对误差为10.94%.研究结果表明, 激光诱导击穿光谱技术能够准确的检测农产品中重金属含量, 为农产品的安全检测提供技术方法. 关键词： 激光诱导击穿光谱 Cd 定量分析 偏最小二乘法     

Point pattern matching based on kernel partial least squares

Point pattern matching is an essential step in many image processing applications.This letter investigates the spectral approaches of point pattern matching,and presents a spectral feature matching algorithm based on kernel partial least squares(KPLS).Given the feature points of two images,we define position similarity matrices for the reference and sensed images,and extract the pattern vectors from the matrices using KPLS,which indicate the geometric distribution and the inner relationships of the feature points.Feature points matching are done using the bipartite graph matching method.Experiments conducted on both synthetic and real-world data demonstrate the robustness and invariance of the algorithm.     

Quantum algorithm for total least squares data fitting

The total least squares (TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the variables. In this work, the TLS problem is transformed to finding the ground state of a Hamiltonian matrix. We propose quantum algorithms for solving this problem based on quantum simulation of resonant transitions. Our algorithms can achieve at least polynomial speedup over the known classical algorithms.     

Quantum partial least squares regression algorithm for multiple correlation problem

Partial least squares (PLS) regression is an important linear regression method that efficiently addresses the multiple correlation problem by combining principal component analysis and multiple regression. In this paper, we present a quantum partial least squares (QPLS) regression algorithm. To solve the high time complexity of the PLS regression, we design a quantum eigenvector search method to speed up principal components and regression parameters construction. Meanwhile, we give a density matrix product method to avoid multiple access to quantum random access memory (QRAM) during building residual matrices. The time and space complexities of the QPLS regression are logarithmic in the independent variable dimension n, the dependent variable dimension w, and the number of variables m. This algorithm achieves exponential speed-ups over the PLS regression on n, m, and w. In addition, the QPLS regression inspires us to explore more potential quantum machine learning applications in future works.     

Near-infrared spectroscopy combined with equidistant combination partial least squares applied to multi-index analysis of corn

Development of small, dedicated, reagentless, and low-cost spectrometer has broad application prospects in large-scale agriculture. An appropriate wavelength selection method is a key, albeit difficult, technical aspect. A novel wavelength selection method, named equidistant combination partial least squares (EC-PLS), was applied for wavenumber selection for near-infrared analysis of crude protein, moisture, and crude fat in corn. Based on the EC-PLS, a model set that includes various models equivalent to the optimal model was proposed to select independent and joint-analyses models. The independent analysis models for crude protein, moisture, and crude fat contained only 16, 12, and 22 wavenumbers, whereas the joint-analyses model for the three indicators contained only 27 wavenumbers.Random validation samples excluded from the modeling process were used to validate the four selected models. For the independent analysis models, the validation root mean square errors (V_SEP), validation correlation coefficients (V_R_P), and relative validation root mean square errors (V_RSEP) of prediction were 0.271%, 0.946, and 2.8% for crude protein, 0.275%, 0.936, and 2.6% for moisture, and 0.183%, 0.924, and 4.5% for crude fat, respectively. For the joint-analyses model, the V_SEP, V_R_P, and V_RSEP were 0.302%, 0.934, and 3.2% for crude protein, 0.280%, 0.935, and 2.7% for moisture, and 0.228%, 0.910, and 5.6% for crude fat, respectively. The results indicated good validation effects and low complexity. Thus, the established models were simple and efficient.The proposed wavenumber selection method provided also valuable reference for designing small dedicated spectrometer for corn. Moreover, the methodological framework and optimization algorithm are universal, such that they can be applied to other fields.     

The quality control of two Pueraria species using Raman spectroscopy coupled with partial least squares analysis

The dried roots of Pueraria lobata (Puerariae Lobatae Radix; PLR) and Pueraria thomsonii (Puerariae Thomsonii Radix; PTR) are medicinal herbs that are used interchangeably in clinical practice, even though their chemical profiles are different. Therefore, the aim of this study was to develop a rapid and non‐destructive method for the quality control of Pueraria species using Raman spectroscopy in combination with partial least squares analysis. Partial least squares‐discriminant analysis (PLS‐DA) was used to differentiate PLR from PTR, whereas partial least squares regression (PLSR) was used to predict the total phenolic content (TPC) and antioxidant capacities of the Pueraria species. Raman spectroscopy revealed that spectral characteristics of starch and polyphenols differentiated the two species, with the PLS‐DA model giving 100% classification accuracy for the tested samples. A significantly higher TPC (p < 0.001), 2,2′‐azino‐bis(3‐ethylbenzothiazoline‐6‐sulfonic acid) (ABTS) radical scavenging activity (p < 0.001) and cupric reducing antioxidant capacity (CUPRAC; p < 0.001) were observed for PLR as compared to PTR. The high ratio of performance to deviation values (TPC: 9.84; ABTS: 7.11; CUPRAC: 7.13) indicated the PLSR models were robust for predicting TPC and antioxidant capacities. The loading plot revealed that the content of starch and polyphenols were important factors in differentiating PLR from PTR and predicting TPC and antioxidant capacities. The results demonstrate that Raman spectroscopy coupled with chemometrics is a rapid method for the quality control of PLR and PTR. These methods can be applied as a template for the quality control of other herbal medicines and products to promote the correct identification of herbs for clinical practice. Copyright © 2015 John Wiley & Sons, Ltd.     

基于小波核偏最小二乘回归方法的混沌系统建模研究

基于核学习的强大非线性映射能力,结合用于回归建模的线性偏最小二乘(PLS)算法,提出一种小波核偏最小二乘(WKPLS)回归方法. 该方法基于支持向量机使用的经典核函数技巧,将输入映射到高维非线性的特征空间,在特征空间中,构造线性的PLS回归模型. PLS方法利用输入与输出变量之间的协方差信息提取潜在特征,而可允许的小波核函数具有近似正交以及适用于信号局部分析的特性. 因此,结合它们优点的WKPLS方法显示了更好的非线性建模性能. 将WKPLS方法应用在非线性混沌动力系统建模上,并与基于高斯核的核偏最小二乘 关键词： 小波核 偏最小二乘回归 混沌系统 建模     

遗传算法与最小二乘法在实验数据处理中的对比研究

采用遗传算法拟合甘油的黏度随温度的变化公式,并将得到的经验公式与采用传统的最小二乘法得到的公式比较.发现在处理某些非线性拟合问题时,采用最小二乘法并非最好,遗传算法得到的结论更优,方法也更简单.     

Multivariate analysis of PECVD data

Basic research in PECVD aims at disclosing relations between quantities determining the plasma performance and solid-state properties of deposited thin films. Linear concepts of multivariate analysis provide a simple and very useful first approach to this goal. In this paper we apply the techniques of principal component analysis, canonical correlation and group analysis to recently published PECVD data. We also touch upon experimental strategy.     

A weighted least squares method for circle fitting to frequency response data

Despite the recent development of powerful multi-degree of freedom curve fitting programs the advent of the microcomputer has meant that there is still scope for improvement of simpler single degree of freedom models. A weighted least squares curves fitting method, based on a well known conformal mapping, is described. This method is shown to have important theoretical advantages over some established methods.     

ICP-AES测定高浓度基体下杂质元素的偏最小二乘法研究

建立了ICP-AES测定高浓度基体中微量杂质元素的偏最小二乘方法(PLS)。研究表明,PLS能有效校正高浓度基体干扰引起的测量误差,比多元光谱拟合法(MSF)能承受的基体浓度更高。当基体与杂质的含量比为1 000∶1～20 000∶1时,该方法的加标回收率在95%～105%之间。对于干扰效应与基体浓度呈非线性相关的体系,普通PLS的预测准确度不高,但使用基于样品浓度矩阵变换的偏最小二乘法(LIN-PPLS),则明显改善了预测的准确度。分别用MSF、普通PLS和LIN-PPLS对水系沉积物国家标准物质GBW07312中的Co,Pb和Ga进行测定,结果表明,LIN-PPLS的预测准确度优于普通PLS,而普通PLS的预测准确度优于MSF。     

Properties of integral least squares method

A new modification of the least squares method (LSM) is proposed. The main idea is to consider the fitting parameters β _i as independent random variables with a certain distribution density F(β₁, β₂, ..., β _k ; φ₁, ..., φ _m ), which depends on a set of m experimental points φ _j . Within this approach, the estimates of the parameters minimize squared deviations and are equivalent to means of the probability distribution = = ∫β _i F(β₁, β₂, ..., β _k ; φ₁, ..., φ _m )dβ₁ dβ₂...dβ _k . Original Russian Text ? I.D. Gorlachev, B.B. Knyazev, A. Kuketayev, F.M. Pen’kov, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 2, pp. 257–260.     

Artificial neural networks versus partial least squares and multivariate resolution-alternating least squares approaches for the assay of ascorbic acid,rutin, and hesperidin in an antioxidant formulation

Abstract

This study was concerned with the assay of ascorbic acid (ASC), rutin, and hesperidin (HES) in their combined formulation using a multivariate approach. Three chemometric-assisted spectrophotometric models namely: partial least squares, multivariate curve resolution-alternating least squares, and artificial neural networks were developed and validated. The quantitative analyses of all the proposed models were assessed by percentage recoveries, root mean square error of prediction, and standard error of prediction. The proposed models were used in the range of 10.0–70.0, 2.0–10.0, and 2.0–10.0?µg mL^?1 for ASC, rutin, and HES, respectively. In addition, correlation coefficients between the pure and estimated spectral profiles were used for the qualitative analysis of a multivariate curve resolution-alternating least squares model. Artificial neural networks showed higher speed and methodological simplicity over the other two models. These models presented powerful multivariate statistical tools that were applied to the analysis of the combined dosage form in the Australian market. They have the ability to overcome difficulties such as colinearity and spectral overlaps. Statistical comparison between the proposed and reported methods showed no significant difference. The proposed methods can be used for the routine analysis of the studied drugs in quality control laboratories.     

紫外光谱结合偏最小二乘法测定手性药物对映体的组成

利用R和S对映体与蔗糖间手性作用方式不同而产生的紫外吸收光谱差异分别测定了甲霜灵和布洛芬手性对映体的组成。采用偏最小二乘法(partial Least Squares,PLS)分别建立甲霜灵和布洛芬手性对映体摩尔分数的定量模型,并采用外部检验对模型效果进行评价。甲霜灵-蔗糖体系中精甲霜灵摩尔分数的定量模型校正集的决定系数R2为99.98%,标准偏差SEC为0.003;外部检验集的预测值与理论值的相关系数为0.999 8,标准偏差SEP为0.000 4,相对标准偏差RSD为0.05%。布洛芬-蔗糖体系中S-布洛芬摩尔分数的定量模型校正集的决定系数R2为99.82%,标准偏差SEC为0.007;外部检验集的预测值与理论值的相关系数为0.998 1,标准偏差SEP为0.002,相对标准偏差RSD为0.2%;结果表明本方法可以用于两种药物对映体组成的快速测定,对手性药物质量分析与控制有重要的参考价值。     

ANAFOR: application of a restricted linear least squares procedure to NMR data processing

Experimental data collection time in multidimensional nuclear magnetic resonance experiments can be significantly decreased if the lineshapes of all the components of one of the ID summations of the spectrum are known. When this condition is fulfilled, a simple linear least squares fit of the time-domain signal taking the lineshapes into account not only allows saving time in data collection, but also improves sensitivity and resolution. The reliability of the proposed procedure is carefully addressed in the particular case of Lorentzian lines. This strategy applied to a 3Q-REDOR experiment reduced experimental time by a factor of 6.     

Multivariate data analysis for Raman spectroscopic imaging

This article reviews the analytic techniques for Raman spectroscopic imaging with emphasis on chemometrics. Key information included in Raman spectra is often distributed broadly throughout the dataset. It is possible to condense the information into a very compact matrix representation by a chemometric technique of factor analysis such as principal component analysis (PCA) or self‐modeling curve resolution (SMCR). PCA yields two matrices called scores and loadings which complementarily represent the entire features broadly distributed in the dataset. This concept can be further extended to other forms of data transformation schemes, including bilinear data decomposition based on SMCR analysis. SMCR offers a firmer model which is chemically or physically interpretable. The information derived from these techniques readily brings useful insight into building a mechanistic model for understanding complex phenomena studied by Raman spectroscopy. Illustrative examples are given for applications of both PCA and SMCR to Raman imaging of pharmaceutical tablets. Copyright © 2009 John Wiley & Sons, Ltd.     

最小二乘法线性拟合中参数的确定问题

指出一些文献在讲术最小二乘法线性拟合中参数确定时存在的问题。     

Selection of optimal combinations of inputs in a partial least squares model for prediction of soil organic matter

Abstract

Partial least squares model is widely used in estimation of soil physical and chemical parameters such as soil organic matter and moisture content, due to its advantages in dealing with collinearity of variables like hyperspectral reflectance. However, it is hard to determine optimal combination of partial least squares model input for soil organic matter prediction since there are lots of possibilities such as, different mathematical transformation of spectral reflectance, wavelength ranges, and spectral resolution. Laboratory hyperspectral reflectance of soils in Songnen plain were analyzed in this study, and the orthogonal experimental design method for deriving optimal combination of input variables for soil organic matter prediction models was introduced. For intercalating orthogonal experimental design table, five different levels which commonly used by researchers were assigned to factors. Results show that the optimal combination input for single black soil is using the derivative logarithmic reciprocal reflectance in the wavelength range selected by multiple stepwise regression at a spectral resolution of 5?nm (R²=?0.95, RMSE?=?0.21, and RPD?=?4.49), and different soils is using continuum removed in the wavelength range selected by MSR at a spectral resolution of 5?nm (R²?=?0.77, RMSE?=?0.74, and RPD?=?2.08). With optimal combination input, the partial least squares model prediction ability was evaluated as excellent for single black soil, possible for different soils. This study illustrates the orthogonal experimental design method can be an effective way to identify the optimal input variables of a partial least squares model for soil organic matter prediction, and multiple stepwise regression can be a preprocessing step to reduce hyperspectral data redundancy before using partial least squares to predict soil organic matter. Overall, this study provides a new approach for determining optimal input of partial least squares predicting model.